Preheat the oven to 450°F. Line two baking trays with parchment paper or reusable silicone baking mats.
First, make the dough. Place all the dry ingredients in the bowl of a stand mixer fitted with the paddle or dough hook attachment, then add the olive oil and water. Mix on medium-low speed for 3 to 5 minutes, until the dough is smooth and pliable. Alternatively, stir together all the ingredients in a bowl, then knead by hand for 5 to 10 minutes. Divide the dough into two pieces, roll into balls, and brush with olive oil to prevent the dough from drying out. Set aside and allow the dough to rest while you prepare the pesto.
To make the pesto, place the basil, pine nuts or walnuts, garlic, miso, and salt in the bowl of a food processor, and pulse to finely chop, Scrape down the sides of the bowl with a spatula, then turn the machine on and stream in the olive oil. Process until mostly smooth. Add the nutritional yeast and pulse briefly to combine.
Place a ball of dough on one of the prepared baking trays and flatten slightly. Use a rolling pin to roll out the dough to a thickness of roughly 1/4-inch, or until about 8 to 10 inches in diameter. (It works best to remove the parchment or silicone baking mat from the baking tray before rolling the dough, then transferring back to the tray when the dough is rolled.) Repeat with the second ball of dough. Use a fork to prick the crust all over, then transfer to the oven. Bake for 5 minutes.
Remove the par-baked crust from the oven, and spread with pesto. (Depending on the size of your pizzas, you may have extra pesto - try freezing it into ice cube trays for later.) Sprinkle evenly with grated cheese and top with the tomatoes. Return the trays to the oven and bake for 10 to 12 additional minutes, until the cheese is melted and the crust is firm and starting to brown.
Remove from the oven, allow to cool slightly, and garnish with optional basil leaves. Enjoy immediately.