On a clean work surface, pile the flour into a mound. Make a well in the center of the flour and add the egg yolks and kosher salt into the well.
Using a fork, gently whisk the egg yolks, gradually incorporating flour from the edges of the well into the mixture. Continue until the dough starts to form.
Add water, a teaspoon at a time, as needed, to help the dough come together. Once the dough holds its shape, knead it by hand for about 10 minutes until smooth and elastic.
Lightly flour your work surface and roll the dough out to a thickness of about ⅛ inch. If the dough begins to stick, gently lift it and dust the surface underneath with more flour.
Using a pizza cutter or sharp knife, cut the dough in half widthwise. Then, cut each half into ¼-inch-wide strips lengthwise to form noodles. Gather the strips into small piles and let them rest for a few minutes.
Cook immediately or freeze for later use.