Put 2 cups of flour onto a large plate and make a well in the middle. Add 1 egg, ⅓ of the salt and 2 Tablespoons of water to the well.
Using a fork, lightly whisk the egg, water and salt while bringing in some of the flour from the inside edge of the well.
Repeat the same process with the remaining eggs, salt and water and incorporate all of the flour until you have a sticky, but loose dough.
Add 1-2 Tablespoons of additional flour and work it into the dough until it is no longer sticking to your fingers. I usually use about 2½ cups of flour.
Flour a large, clean work surface and place the dough onto the surface. If the dough is still sticky, you can add a little more flour. Begin working the dough by folding it towards you and then turning it and folding it again. This is similar to kneading bread dough.
The dough is done when it is no longer sticky and it's a smooth dough ball. Wrap in plastic wrap and let rest for 30 minutes.
Rolling out the Dough
Roll out the dough on a floured surface with a rolling pin until it is your desired thickness. I like to roll it to about ¼" thick, which is just thin enough to start to see my hands through the dough. The dough should be in the shape of a large rectangle.
Cutting the Noodles
Lightly flour the top of the dough sheet. Roll up one of the short ends until you reach the middle. Then roll the other end until it meets the center. It will look like a scroll.
Cut the scroll with a sharp knife to make the noodles. How far apart you space the cuts will determine their thickness. Place the flat side of your knife under the cut scroll and flip so the dull side of the knife is pointing up. Your noodles will unroll themselves.
Place the noodles back on the work surface and cut to desired length. Toss the noodles in a little bit of flour so they won't stick to each other. Store in an airtight container in the refrigerator for 1-2 days or you can use them right away.
You can also freeze the noodles. I recommend lining a tray with parchment paper and spreading the noodles out so that they freeze separately. Once frozen, you can put them into a freezer bag.