In a large bowl, stir together the starter, water, and eggs.
In a separate bowl (I used my stand mixer), mix together all dry ingredients; all of the flours, salt, xanthan gum, and sugar.
Add the oil or butter to the dry ingredients and mix until well blended.
While the mixer is on low, slowly pour the liquid ingredients into the dry ingredients. If you do it all at once or too quickly, you may end up with lumpy dough. Pour just slow enough that it can be gradually mixed, but not so slow that it takes you more than a minute. If you are mixing by hand, pour it in approximately a cup at a time and mix as you go.
Let the dough sit out in a warm place for at least a few hours, preferably 6-8.
You may then take out approximately 1/4 of the dough to bake if you'd like and place the rest in the refrigerator for later use.
When baking, gently place the dough on parchment paper if you have any (I don't and it worked fine) on a flat surface. You want to be careful not to disturb the dough too much so that it keeps the air bubbles intact from the sourdough action. Use wet hands to smooth it out if you'd like, and let it rest for 4-8 hours.
Preheat the oven to 500 degrees F with a cast iron dutch oven. You can also use a 1 1/2 quart Corningware casserole dish with glass lid. I used the latter (like this one) since I don't have the dutch oven and it works just fine.
Once preheated, very gently slice the top of the loaf a few times with a serrated knife and place into the preheated pan.
Bake for 15 minutes.
Take off the cover and reduce heat to 450 degrees and bake for another 20 minutes.