Add the flours and xanthan gum to a medium bowl and use a fork to combine. Add the eggs and oil continue mixing until most of the egg has been incorporated.
Get your hands in there and thoroughly squelch the dough through until mostly smooth. Add the water, a teaspoon at a time, until you have a firm ball but smooth of dough and no errant bits of flour left in the bowl. Cover the dough and allow to rest for 5-10 minutes.
Generously flour your workbench and rolling pin with tapioca flour. Tear about a golf ball size dough off at a time and use your rolling pin to flatten it sufficiently for the thickest setting of your pasta machine. Once it goes through smoothly, place it on the next lowest setting to begin thinning the dough out.
As I mentioned, I like to cut this dough while reasonably thickly so that my noodles are thicker. When you are happy with the thickness (keeping in mind that they expand during cooking) thread the pasta sheet through your spaghetti cutter. Repeat this process until you have used all the dough.
To cook the noodles, bring a really well salted medium pot of water to the boil. Add the noodles and cook for 2-3 minutes. Test a noodle and see if they are done to your liking and go from there. Drain when cooked, then serve with your sauce or toppings of choice.
You can keep cooked noodles in the fridge for a few days, or freeze uncooked noodles. To do this, pile them into nests and freeze them in an airtight container. Cook them straight from frozen, allowing a little extra cooking time.