In a large mixing bowl, combine the all-purpose flour and salt. Make a well in the center and add the egg yolks, the whole egg, and 5 tablespoons of water. Using a fork, gently mix the ingredients together until a shaggy dough begins to form.
Transfer the dough onto a floured surface. Knead the dough for about 5-7 minutes, or until it becomes smooth and elastic. If the dough feels too dry, add a little more water, one teaspoon at a time, until it reaches the right consistency.
Wrap the kneaded dough in plastic wrap or cover it with a damp cloth. Allow it to rest for at least 30 minutes at room temperature.
After resting, divide the dough into two portions. On a floured surface, roll out one portion at a time to your desired thickness, usually about 1/8 inch thick.
Using a sharp knife or pasta cutter, cut the rolled-out dough into strips. You can create fettuccine-style noodles or experiment with different widths.
Bring a large pot of salted water to a boil. Carefully add the cut noodles and cook for 2-4 minutes, depending on the thickness.
Once cooked, drain the noodles in a colander. Toss them with a bit of olive oil or butter to prevent sticking, and they’re ready to be served.