It's tempting to think that true Italian cooking must be complicated. If you've ever eaten good Italian food and tasted the depth and richness of a good sauce, or the delicate flavor and texture of a handmade pasta, it's understandable. Fortunately for you, you'd also be wrong. Italian cooking is not difficult, but you need to put your heart into it.
Techniques
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No matter which region you're cooking from, the processes of cooking most Italian foods aren't different from cooking methods you may already know. Italians pan-roast, oven-roast, sautee, braise, broil, grill, pan-sear, simmer and bake.
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The main thing that's different is that in most cases, Italians are not content to settle for pre-made ingredients bought at the store. Instead, they want what's freshest and tastiest for their tables, no matter what that might be. This holds true for pasta as well. While it's usually served as a first course rather than as a main dish like it is here, fresh pasta is a very important thing to learn how to make.
The basic recipe from which most pasta is made is simple, calling only for semolina flour, eggs, extra virgin olive oil, water and salt. Traditionally, you should measure out the flour onto your counter and make a well in the middle. Next, crack your eggs into the center and sprinkle salt and olive oil on top. Using a fork, beat the flour from the sides of the well into the eggs a little at a time. Continue mixing until you have dough. If it gets too dry, add water a tiny bit at a time and continue working the mixture by hand until you have smooth, slightly sticky dough. Keep extra flour on hand to sprinkle on your counter.
Equipment
Here's where you have a choice: you can roll your dough out by hand, but it will take longer and you may find it frustrating. Italian grandmothers usually have rolling pins that are rather thick wooden dowels that they use for this purpose; you can buy these in specialty shops. You can also buy hand-crank or electric pasta rolling and cutting machines, and these are what most people use today. The hand-crank ones are made of metal, usually clamp to your tabletop and are fairly easy to use. Cutters for various shapes of pasta attach to these, so that you can run sheets of fresh pasta through them directly after they're made.
One word of caution: never submerge your metal pasta machine in water to clean it. Wipe with a damp cloth if necessary; most frequent users simply brush the flour off and then put their machines away after each use.