The idea of a Spanish tortilla is a romantic one. About a cup of great olive oil seduces slices of potatoes into a crispy, creamy, naughty open-faced omelette. Something you'd nibble a thin slice of from a plate atop your tiny glass of sherry while mingling about a tapas bar. While sporting a luxurious mustache. In reality, it's a nice excuse to eat potato chips for dinner under guise of serving a frugal meal. While pretending to have a luxurious mustache.
The easiest way to slice potatoes paper-thin without a proper expensive mandolin slicer is to use a vegetable peeler. Peel the potatoes, then head to your favorite small non-stick pan and keep peeling. Hold the potato towards the pan though because the starch will flip all over your range. Unless you have a white cooktop. This is one of the few times you win the clean-looking-but-not-really-clean kitchen award. And don't go crazy here; when you get to the bottom there will be a little nub that you just can't get any smaller without risking your fingers. ER visits aren't frugal.
Once you've flipped it (without having to stop and extinguish a grease fire), season this side liberally with salt, pepper and cayenne pepper. Continue cooking (add oil if necessary to facilitate browning) until the other side is nice and brown. If you like, you can stop here and have a great side dish: potato chip platter. (Really; serve with Sriracha and ketchup.) But to feel better about calling it a meal, once the potatoes on the bottom are browned, beat an egg and pour it over the top. Cover and turn down the heat. Cook until egg is set.
Or sherry and fake mustaches if you're feeling fancy.