EE encompasses a lot of "engineering that takes hard math" at a professional and research level (similar to "hard CS," just different fields of math), so it is very hard to do as an undergrad, when your background in complex analysis and E&M is weak. Early classes on circuits in EE will usually take shortcuts using known circuit structures and simplified models. The abstraction underneath the field of analog circuits…
But aren't there a lot of actual hardware products that are "simple circuit blocks connected to a microcontroller"? Like a toaster, shaver, keyboard, etc. If that's not "work in EE" then what is it classified under? It's not CS either.