Combine flour, xanthan gum, guar gum, and salt in the bowl of a stand mixer fitted with the paddle attachment; mix well. Make a well in the center; add egg yolks and egg and mix on medium speed until well combined, about 2 minutes. Add oil and water, 1 tablespoon at a time; mix well.
Switch to the hook attachment; knead on medium speed until dough comes together, about 3 minutes. Place dough in a greased bowl; cover and let stand for 20 minutes.
Divide dough into 4 equal parts. Roll each piece over a floured surface and make pasta strips of desired width using a pasta machine or a sharp knife.