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.