Build your flour well on the counter, not in a bowl
Create a well in the middle of the flour mound, so there are walls a little less than an inch thick. Crack all 3 eggs into the well.
Mix it together
Whisk the eggs with a fork and gradually whisk in the flour from the bowl sides in little circles (inside out) until it thickens to a shaggy consistency. As the mixture loses its liquid consistency and becomes shaggy, put the fork down and squish the remaining flour with your hands. If any egg gets out, quickly scrape it back in.
It will look messy, lumpy, and sticky. Don't add more flour. Just knead it and see the transformation.
Knead it for real 8 to 10 minutes, set a timer
Use the heel of your hand to push the dough away, fold it over, and turn the dough a quarter turn. It's done when the dough is smooth, a bit tacky but not sticky, and springs back slowly when you touch it.
Rest it and reset your kitchen
Gently round the dough into a smooth ball, wrap it in plastic wrap, and rest at room temperature for 30-60 minutes. Don’t skip this. The gluten is tight from all the kneading, and needs to relax.
While it rests, sweep your work surface clean, dust it with flour, and have a dusted tray ready for the pasta.
Roll and cut
Divide the dough in half (store the other half wrapped). Fresh pasta dries out fast.
Flatten it with your hand and roll it out from the middle, turning often, until it's an ⅛ inch thick (you should be able to see the shadow of your hand through it, but it shouldn't tear when you lift it). You could use a pasta machine for this step if you have one. Cut into ½ inch wide, 3-4-inch-long strips. Irregularity is fine.
If it keeps springing back, cover it and let it rest again for 10 minutes. A rested dough rolls easily. An under-rested dough fights you.
Shape it
Take a strip and roll it between your palms. Repeat until all of the strips are shaped.
Your pieces will be different shapes. If strips tear, be gentle. Press and roll, no pushing.
Prep Your Sauce
Have your sauce warm and ready to toss pasta into a saute pan with.
Cook it for about 4 minutes, don't walk away
Large pot, lots of water, boiling. Season to taste like seawater; it is the only time you can season the pasta itself.
Put in the pasta and stir. Homemade pasta rises to the surface when cooked. Reserve at least a cup of pasta water on the side. Milky, starchy, and probably the most helpful thing for your sauce.
Strain and back to the sauce. Don't let it sit.
Mantecare
Toss the pasta hard in the sauce to emulsify it into a shiny coating. Add some pasta water, toss hard, and the sauce becomes part of the pasta instead of just something you pour on.