Pesto
Using a mortar and pestle (or other improvised device), crush some of the sweet basil, "feeding" it small amounts of olive oil while crushing. Grate the clove of garlic into the pesto and continue crushing. Add all of the basil and crush the mix into a semi-paste.
Dough and Pizza
In a mixing bowl, combine water, yeast, and one tablespoon of olive oil. Mix to homogenize! Set aside.
Combine whole wheat and white flour in a separate bowl. Add the pesto into the flour and mix thoroughly.
Add 1-2 cups of the flour to the water/yeast/oil bowl. Mix, adding the rest of the flour in intermittent cupfuls.
On a lightly floured surface, knead the dough for about 5 minutes.
Spread some olive oil around an empty bowl to lightly coat the surface. Use spray-on oil if you want to conserve your nicer oils.
Place a cloth over the bowl and store at room temperature for about 2 hours.
After dough rises, preheat oven to 400 degrees Fahrenheit.
In a deep 8x13-inch baking pan (or a pan of similar size, but at least 2 inches deep), press out the dough to fill the bottom of the pan.
Top with sauce, vegan mozzarella, and toppings. Here's an excellent topping combination I tried that turned out great:
orange bell pepper, shallots, zucchini, vegan pepperoni, and crimini mushrooms
Bake at 400 degrees Fahrenheit for 10-20 minutes, baking dough as desired.