There are a bunch of recipes out there for egg pasta dough, but the most common recipe is a simple combination of flour and eggs. There are many schools of thought when it comes to the ratio of yolks to whole eggs, and what type of flour is best and I plan on addressing each of these in turn, but today I'm going to share with you what I think is the most practical solution*.
If you have a food scale, this is an excellent time to break it out. If not, no problem. Depending on humidity, you may need more or less flour than suggested; making pasta is all about feel - I'm not a big believer in this as an exact science. The following makes 1-2 portions (depending on what you do with it)
100g flour** or just under 3/4 of a cup
1 lg egg + 1 yolk
pinch of salt.
Shape your flour and salt into a mound and make a shallow hole for the eggs and yolk. Beat the eggs with a fork and slowly incorporate the flour into the eggs, trying not to get egg outside the mound. When it seems like the egg cant be beaten without breaking the "puddle" I like to tap flour in from the sides. At this point there is a good chance you will have destroyed your egg puddle, and that's okay, because it shouldn't really be a puddle anymore. This is when you get your hands dirty. I like to push the pile together from the sides then, almost folding the outside edges in and then down; I repeat that motion, alternating between pushing it in from the sides, and from the top/bottom (so both horizontally and vertically) and as the dough gets less crumbly, you can start pressing it into a crumbly ball, see the pictures below, and when you have most of the crumbs in the ball, its time to knead your dough.
I think that kneading the dough, and the resting period after are the one of the hardest parts about making pasta. I'm very fortunate that kneading dough happens to be EXACTLY like wedging clay, which is something I do literally everyday for work. Its a muscle memory thing, so once you do it a few times, or even for a few minutes it gets a lot easier. Kneading the dough is important because it helps does something to the gluten/protien in your dough. As you work it you'll notice it get softer and smoother. In the photos above, the bottom two show the difference after the dough was kneaded for 5 minutes. I would say the basic kneading motion is pressing down the middle of the dough, folding it over, rotating it 45 degrees then repeating that motion while trying to keep it in a ball-ish shape. I will try to figure out how to post a video.
After 5 minutes, the more challenging part comes. The waiting. This is a really important step. It allows the gluten to relax, and the moisture from the egg to be absorbed by the flour particles. Without resting, it will be almost IMPOSSIBLE to roll out your dough, this is when stretchyness happens. Your ball should be wrapped tightly in plastic wrap so it doesn't dry out. I usually let it rest for at least 15 minutes, (20-30 is ideal) but you could let it rest longer, probably for an hour on the counter, after that it should head into the fridge. (when you use it again bring it back up to room temperature) After the 15 minutes you should be amazed at the difference, check out the difference between the last photo above, and the picture below
Its so much yellower, and stretchier; and trust me, its way easier to work with than the un-rested stuff. At this point you'd roll it and shape it, and which we will totally get into it; just not now. Stay tuned for Pasta 101 pt 2 - rolling and shaping.
P.S. So far I've had pretty good luck freezing the dough at this point. Wrap it well in plastic wrap, and to thaw, put it in the fridge. Bring it up to room temperature before rolling.
*Practical in the sense that it doesn't use exclusively egg yolks, some recipes call for literally 20 yolks, and unless you're a HUGE egg white fan thats just not practical for the average home cook. I do plan to "explore yolks" soon watch out for that.
*I've tested semolina, all purpose and 00 flour with this recipe, I wouldn't recommend whole wheat, and haven't gotten around to doing gluten free tests. There's a whole post coming about flour soon, so stay tuned for the deets.