I don't pretend to be a Buddhist or Zen student, but as I understand it the advantage comes from understanding another Buddhist idea, that desire causes suffering.
When you want a big car and you don't have one, you suffer. When you want to keep up with the neighbours and cannot, you suffer. When you desire to be out of the cold, you suffer both coldness and unfulfilled desire. If you released your desire to be out of the cold, you would experience coldness, not suffer it.[1] From that kind of thinking, desiring to solve problems and worrying that you cannot is a suffering. Desiring to solve problems so people look up to you is a suffering. Desiring to make the most out of every moment and not waste time "merely peeling potatoes" because you want to be better, smarter, cleverer, more productive, more important, living a more exiciting or higher status life than people who merely peel potatoes is a suffering.
Go through life from start to finish like a river, the river does not seek to be somewhere else, to do something else, to be more or less than it is. Nor will you escape aging, disease, and death, by thinking about other things while peeling potatoes. Nor will you have a better life by solving problems while peeling potatoes, for everything is body sensations and breathing and seeing and hearing, from the cheapest clothes to the most expensive, from the cheapest hut to the luxuryiest apartment, the lables 'cheap', 'luxury', 'comfortable', 'uncomfortable', 'homely', 'ugly', are labels in our heads taught to us by marketers trying to sow social discord and sell products. You have potatoes to peel, peel them. Attend to the movement of your fingers, the sharpness of the blade, the pulsing of your heartbeat, the firmness of the flesh, the way the peel falls, the mud, the splashing water, the scent of raw vegetable, would it be different if you were peeling Venusian potatoes dressed in Flash Gordon shiny silver spaceclothes in a Dyson Swarm pod? Well, I'd rather someone else peeled the potatoes while I did something more exciting, you say, sitting at your computer reading this on HN having an unexciting life, waiting year after year for your exciting life to start, desiring it, suffering for its lack, sadly aware that you have teeth to brush, hands to wash, food to prepare, possibly potatoes to peel, in the imminent future.
[1] the only way I can make sense of this is to be willing to accept that it may result in physical pain, damage, even the end of your life, and accept that, too. Desiring to prolong your life when you cannot do so, is suffering also. Desire for a healthy body when you are injured, is suffering. If you can go inside out of the cold, do so. Take action, have a preference. But if you cannot, do not. [If you can avoid peeling potatoes, and wish to do that, do so. If you cannot, do not]. Do not add suffering by longing for log fires and blankets and hot tea, and self-chastising for letting yourself get stuck outside, or resenting your coworkers or family who dragged you out, or your bad luck for your bus to be late, and so on. If 'experiencing cold' is your life now, then experience it attentively and do a good job of it. [I believe it goes on that the physical discomfort becomes a sensation like speech becomes noise, and then people have surgeries without anaesthetic not because they can stop feeling sensations but because they can stop desiring to not feel pain, they can experience sensations without labelling them as "pain" and needing them to stop.].