Step 1: In a large bowl, beat the whole egg and the egg yolks together until they are light and slightly frothy.
Step 2: Add the cold water and salt to the beaten eggs, mixing well to combine all the wet ingredients.
Step 3: Gradually add the all-purpose flour to the wet mixture, mixing with a fork or your hands until a shaggy dough forms.
Step 4: Turn the dough out onto a lightly floured surface. Knead the dough for about 5-7 minutes until it is smooth, elastic, and no longer sticky.
Step 5: Form the dough into a ball, cover it with plastic wrap or a damp towel, and let it rest for at least 30 minutes at room temperature. This helps relax the gluten, making the dough easier to roll.
Step 6: Divide the rested dough into two or three portions. On a well-floured surface, roll out one portion of dough as thinly as possible (about 1/8-inch thickness) using a rolling pin.
Step 7: Using a pizza cutter or a sharp knife, cut the rolled dough into strips of your desired width (approximately 1/4-inch wide for classic egg noodles). Gently separate the noodles and dust them lightly with flour to prevent sticking.
Step 8: Bring a large pot of heavily salted water to a rolling boil. Add the fresh homemade egg noodles and cook for 7-9 minutes, or until they are tender yet still al dente.
Step 9: Drain the noodles and serve immediately in your favorite dishes, such as chicken soup, beef stroganoff, or simply tossed with butter and herbs.