For the crust: Put the quinoa in a medium bowl and cover with water by about 1 inch. Cover and refrigerate at least 8 hours or up to overnight.
For the sauce: Meanwhile, heat the olive oil in a large skillet over medium heat. When the oil is hot, add the garlic and cook until the edges are light golden, about 1 minute. Add the tomatoes, oregano, red pepper flakes, 1/2 cup water and salt. Bring to a simmer and cook until thickened, about 10 minutes. Set aside while you make the crust.
Preheat the oven to 425 degrees F with a pizza stone or baking sheet on the bottom rack. Drain the soaked quinoa and rinse well. Line a rimmed half-sheet pan with parchment paper and brush the paper with olive oil. Put the quinoa in a food processor with the oil, baking powder, salt and 2/3 cup water and process to make a smooth, thick batter. Spread the batter into the prepared pan and bake on the hot pizza stone until set, 12 to 15 minutes.
Flip the crust over in the pan and remove the parchment. (If the crust sticks to the sides, run a knife around the edge to loosen.) Bake until the top is crusty and the edges are crisp, about 5 minutes more.
Spread the pizza sauce on the crust, almost to the edges. Sprinkle with the mozzarella and Parmesan and top with the pepperoni. Roughly tear the basil leaves and scatter over the top. Bake the pizza on the top rack until the cheese is melted and bubbly, about 15 minutes. Cut into squares and serve.
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