Some design alternatives:
• Use lime cement rather than portland cement for the mortar. Portland will be damaged over time by the 120° temperature and may spall explosively, causing injury, particularly if you embed nichrome heating elements in it.
• Similarly, don't use plaster of Paris inside the oven. It will also degrade over time at that temperature. Waterglass would work to fix tiles to wood but will foam up when heated if not crosslinked with polyvalent cations from, for example, chalk or iron oxide. Premixed refractory adhesives of this recipe are available from hardware stores in most countries.
• Use insulating fired-clay ceramic rather than cork or wool for insulation. It will need to be thicker but will not outgas volatile organic compounds into your food or degrade over time. Fireclay is not needed for this application; any normal pottery clay body should work. I used a ball clay body. Mix wet organic waste into the clay body at ratios between 1 and 3 parts organics to 1 part clay body before forming bricks and firing in an oxidizing atmosphere. The organics burn out in the kiln, which smells like hell during the firing. Suitable organic wastes include used yerba mate, used coffee grounds, cow manure, or sawdust made from untreated wood.
• Vermiculite or perlite from the garden store is another safe insulation option. A minimal amount of waterglass can hold it in place.
• Similarly, don't use chipboard (OSB) for the oven structure, as suggested in the article. It outgasses when hot, which it will be if you drape a blanket over the oven, as also suggested in the article. A very common type outgasses formaldehyde, which will condense in your food. You don't want to be eating formaldehyde for years. Similarly for most other composite wood products such as particle board and MDF, which at least the article does not specifically recommend. Masonite (high density fiberboard) should theoretically be fine, but I wouldn't risk it.
• Similarly, don't use hot glue as suggested in the article to attach the insulation. It's normally EVA with additives, but isn't specified for continuous operation close to its melting point, and might also outgas things you don't want condensing in your food for hours every day. I'd even be wary of wood glue. Waterglass with a polyvalent cation source should be fine.
• Mortar is porous, so if you want to be able to clean food off of mortar joints between tiles inside the oven, maybe seal it with waterglass. "Grout" is underspecified. You want a material that is food-safe at cooking temperatures; you don't want to go years eating whatever antifungal additives and plasticizers are in hardware-store grout for your bathroom floor, volatilized by oven heat.
• Electric cooking appliances should always include a thermal cutout device for minimal safety. These are cheap and available worldwide including by salvaging them from broken microwave ovens or electric kettles. They're very simple to use. No excuses. (This is mentioned in the "manual" as a "thermal switch", but only as an option, and not in the article.)
• Normally, high-temperature electrical connections should not be soldered as the "manual" suggests doing; they should use crimped or spring connections. Regular 63/37 electronics solder melts at 183°, which the oven as a whole might reach and which the nichrome could easily reach. It also contains lead, which is probably okay in an oven but seems a bit questionable to me, especially embedded inside mortar.
• Alternative methods of thermal energy storage and release seem like they might be worthwhile for this application, in order to lose less energy when not cooking, and in order to sustain an ideal cooking temperature for longer when cooking. Sensible heat storage like this has the disadvantage of constantly losing heat, which is an enormous disadvantage if the appliance is in your kitchen in a hot climate. Phase-change energy storage might be applicable, but I'm not sure what material melts in the right temperature range. TCES is probably applicable, but would need some design work. For example, plaster of Paris heats up to a usable oven temperature when hydrated, but keeping it from coalescing into a solid mass that is difficult to re-dehydrate conveniently. Phase-change or TCES materials might be portable enough to leave out on your balcony or roof terrace until it's time to cook—carrying them inside is not quite as convenient as flipping a switch, but it's far from the same level of hassle as building a wood fire.
• Storing sensible heat in a much thicker brick through which you can later circulate air might be another alternative, like electric night storage heaters. This would probably require a metal fan, but the amount of battery storage required to power the fan is minuscule compared to the amount you would require to power an electric heating element.
One correction. The article says,
"In contrast, an ISEC can be insulated on all sides, making it more energy efficient than a non-electric solar box cooker." This is arrant nonsense. Non-electric solar box cookers are typically over 50% efficient; retail solar photovoltaic panels are at best 24% efficient, so the efficiency of a solar cooking system that uses a retail PV module to capture sunlight is at best 24% minus the heat leakage through the insulation. (But to me it seems like nonsense to worry about efficiency in a context like this, since sunlight is free.)
Kris de Decker has an established practice of ignoring or denying indisputable factual errors like this when they are pointed out to him, so I fully expect this article to also remain permanently in error. I'd be delighted if he proved me wrong on this.