In a blender or food processor, place the chopped zucchini and blend until as smooth as possible. The zucchini may be pureed and stored in a sealed container in the refrigerator for at least 2 days before proceeding with the rest of the recipe.
In a large bowl, place the all-purpose flour, xanthan gum, tapioca starch/flour, baking powder, and salt, and whisk to combine. Add the vegetable shortening and toss it in the dry ingredients.
With the tines of a large fork, break up the shortening into small pieces about the size of small peas. Create a well in the center of the mixture, and add 3/4 cup (6 fluid ounces) of the pureed zucchini. Mix to combine.
The dough will come together and be thick. Press together into a ball, cover with a moist tea towel, and allow to sit for about 20 minutes. The dough will stiffen a bit as it absorbs more of the moisture.
Heat a 10- or 12-inch cast-iron skillet over medium-high heat.
Divide the dough into five pieces. Begin with one piece of dough, and cover the rest with a moist tea towel to prevent them from drying out. On a lightly floured surface, with a rolling pin, roll out the first piece of dough until it is a bit more than 1/8 inch thick (as compared to the regular recipe for gluten free flour tortillas, these can be a bit harder to roll very thin and still be stable enough to transfer to the skillet).
Cut out as many rounds as you can (should be three or four) with a 6- or 8-inch metal cake cutter.
Stack the raw tortillas on top of one another, dusting lightly with flour between them, if necessary, to prevent them from sticking.
Gather the scraps and set them aside. Repeat with the remaining pieces of dough, including gathering and rerolling all of the scraps together.
Once all the tortillas have been rolled out and cut, place them one at a time in the center of the hot skillet and cook on one side until bubbles begin to appear on the top surface and the tortilla darkens in color a bit on the underside (about 45 seconds).
Flip the tortilla over with a wide spatula, and cook on the other side until more bubbles form and the tortilla darkens in spots on the underside (about another 45 seconds).
Remove the tortilla from the pan, place on a moist tea towel, and cover gently. Repeat with the remaining tortillas.
Using the tortillas.
They can be used right away
They can be placed, still wrapped in the towel, in a plastic bag to seal in the moisture and used within a few hours; or
They can be cooled completely, wrapped very tightly in a freezer-safe wrap and stored in the freezer for at least 2 months. When you are ready to use frozen tortillas, defrost at room temperature and then refresh in a hot, dry skillet to restore pliability.