On a clean work surface, measure and combine the 2 cups all-purpose flour and 1 3/4 teaspoons salt; pile into a mound and make a well in the center.

Add the 3 large egg yolks and the 1 large whole egg into the well.

Using a fork or your fingertips, break the eggs in the well and begin pulling in flour from the sides a little at a time until the mixture becomes shaggy.

Add the 5 tablespoons water gradually, one tablespoon at a time, incorporating it with your fingers or the fork until the dough comes together; if the dough is still too dry after the 5 tablespoons, add additional water sparingly, a little at a time, only until it holds.

Gather the dough into a ball and knead by hand on the floured surface for about 10 minutes, until it feels smooth and elastic.

Wrap the dough in plastic wrap or cover with a bowl or clean towel and let it rest for 10 minutes at room temperature.

Lightly flour the work surface and a rolling pin. Roll the rested dough into a rectangle about 1/8 inch thick.

Lightly flour the top of the rolled dough to prevent sticking, then cut into strips 1/8 to 1/4 inch wide using a knife or pizza cutter.

Gently separate the cut noodles and toss them lightly with a little flour to keep them from sticking together.

Bring a large pot of water to a rolling boil.

Add the fresh noodles to the boiling water and cook for 2 to 4 minutes, checking for tenderness; cooking time will depend on thickness.

Drain the noodles and serve immediately.