In a large mixing bowl, combine the gluten-free flour, xanthan gum (if required), tapioca starch, and fine sea salt. Mix thoroughly to ensure even distribution of the ingredients.
Create a well in the center of the flour mixture. Add the eggs, egg yolk, and water into the well.
Gradually incorporate the flour mixture into the wet ingredients using a fork or your fingers until a shaggy dough forms.
Transfer the dough to a clean, lightly floured surface once it begins to come together. Knead the dough for 5-7 minutes until it becomes smooth and elastic. Adjust the dough consistency by adding a little more water if too dry or a sprinkle of gluten-free flour if too sticky.
Shape the kneaded dough into a ball and cover it with plastic wrap. Allow it to rest at room temperature for about 30 minutes to hydrate the gluten-free flour and relax the dough.
After resting, divide the dough into 4 portions to make handling easier. Flatten each portion into a disk using your hands.
Lightly flour a parchment paper and rolling pin with gluten-free flour. Roll out each portion of dough into a thin rectangular sheet, approximately 1/16 to 1/8 inch thick.
Cut the rolled-out dough into strips and repeat the rolling and cutting process with the remaining dough portions.
To cook the gluten-free egg noodles, bring a large pot of salted water to a rolling boil. Add the noodles and cook for approximately 2 minutes, or until they reach al dente texture. Drain the cooked noodles and serve immediately with your preferred sauce or toppings.
Notes
Use the spoon & level method to measure your gluten-free flour. Spoon the flour into your measuring cups and level it off with a knife. This stops the flour from packing down into the cup.
Add more water if the dough is too dry, or add more flour if it's too sticky.
To Store: Cover uncooked noodle dough and refrigerate for up to 24 hours before using. Let the dough come to room temperature before shaping into noodles.
To Freeze: Cut the noodles to shape and freeze them flat on a baking sheet. Once frozen, transfer to a freezer-safe bag or container for up to 2 months. Cook from frozen and add a few minutes extra to the cooking time.