Cookin' Česky style #3: Tomaš's College-boy pasta sauce

Our recipe today comes from the cabinets of apparently every Czech college student. Before, I think I talked about how a lot of Czech cuisine is food from other countries, just "Czech-ified," and here's your perfect example. I wanted to know how to make this because unlike the pasta I make (using sauce from a jar), this stuff tastes great reheated (we made enough for an army last night, or as Tomaš said, enough for his lunch for the next five days).

For about 700g of pasta:
1 big yellow Onion (diced)
Sunflower oil (or olive oil)
5 cloves garlic (diced, but chunky)
Sweet paprika
Sharp paprika
Salt/pepper
280g tomato paste
Lots and lots of eidam cheese (or parm) (grated)
OPTIONAL: rosemary, oregano, basil, or any other spices you want

Dice up the onions and garlic and sauté them in the oil until the onion is transparent (or “pink” as they say here). Add about 5 knife-fuls of sweet paprika, a pinch of sharp paprika, and a little pepper. Sauté it a bit longer, but not too hot (so you don’t burn the paprika). Add the tomato paste and an equal serving of water and leave the whole thing to boil, covered, stirring every so often.

Pour it over hot pasta, and serve it with a lot of cheese on top.