Proper lasagna actually doesn't require all that many ingredients. You just make the ragu - put a couple of tins of plum tomatoes through a sieve, using say the back of a spoon to push things through. You add that to your diced or minced beef that's been sealed, add in half a cup of good red wine, and your seasonings, such as garlic, a touch of salt, herbs (don't go overboard), maybe some finely chopped onion. You then make the beschamel sauce, which is just a roux sauce of flour mixed with butter and then turned into a creamy sauce with milk. You can get pre-made pasta sheets (much better to buy the fresh ones rather than dried), or make them from scratch. In your dish of choice, after letting the ragu cook for a while, you then alternate between sheets of pasta, the ragu, the beschamel, and slices of mozzarella (adding extra mozzarella I didn't know of until I went to Roma last year but now it's what I always add). Between the layers, you can also add a light sprinkling of Parmigiano (Parmesan cheese).
Italian carbonara is also another really simple recipe, although it can be tricky to master. In carbonara, there is actually no cream, and absolutely no wine (I think it a huge no-no when I see supposedly 'Italian' restaurants doing this). What most people think of as being carbonara is a mash-up of a la crema and carbonara. In a real carbonara, you just have the raw egg added on top of the cooked pancetta and pasta, the heat switched off. You add a tiny dash of olive oil to the egg to help give it a bit of moisture and stop it drying out too much as the egg cooks a bit from the residual heat. If you let it become like scrambled egg it's over cooked. You can add a bit of black pepper, maybe some parsley, and maybe some garlic, or Parmigiano to season it. That's all there is to it.