In a large mixing bowl, combine gluten-free flour, xanthan gum (if needed), tapioca starch, and fine sea salt. Stir to mix evenly.
Create a small well in the center of the dry ingredients. Crack in the eggs, add the yolk, and pour in the water.
Using a fork (or your hands), gradually incorporate the dry ingredients into the wet until a rough dough forms.
Transfer the dough to a clean, lightly floured surface and knead for about 5-7 minutes. The dough should feel smooth yet slightly tacky.
Wrap the dough tightly in plastic wrap and let it rest at room temperature for 30 minutes.
Once rested, divide the dough into four portions. Flatten each piece into a small disk for easier rolling.
Dust a surface and rolling pin with gluten-free flour. Roll each portion until it's about 1/16 to 1/8 inch thick.
Cut the rolled dough into thin strips of your desired width to create noodles. Repeat with the remaining dough portions.
To cook the noodles, bring a pot of salted water to a boil. Add the noodles and cook for about 2 minutes, or until tender but firm to the bite.
Drain the cooked noodles and serve immediately with your favorite sauce or toppings.