Make the pesto: Add basil, walnuts, Parmesan, and garlic to a food processor. Pulse until roughly chopped. With the motor running, drizzle in olive oil, lemon juice, salt, and pepper. Blend until smooth. Taste and adjust seasoning. Set aside.
Preheat your oven to 475°F (245°C) and let it heat for at least 15–20 minutes. Grease a pizza pan or baking sheet with ½ tablespoon olive oil and dust with cornmeal.
Shape the dough: On a lightly floured surface, stretch the dough into a 12-inch circle about ½ inch thick. Transfer to the pan and crimp the edges to form a rim.
Top the pizza: Dimple the dough surface with your fingertips. Brush with the remaining olive oil. Spread all the pesto evenly, then add mozzarella, spinach, and cherry tomatoes.
Bake for 14–16 minutes until the crust is deep golden brown and the cheese is bubbly.
Finish and serve: Scatter fresh basil over the hot pizza. Add red pepper flakes and extra Parmesan if desired. Slice and serve immediately.