To prepare the pesto, combine the fresh basil leaves, pine nuts, parmesan, and garlic in a food processor or high-powered blender. Blend until coarsely chopped. Scrape down the sides, then slowly stream in the olive oil, add lemon juice, and season with salt. Continue blending until the mixture is smooth and cohesive, with a spreadable texture. For a thinner pesto, stir in an extra drizzle of olive oil. Taste and adjust seasoning with black pepper, or add more lemon juice or salt if needed. Transfer to a small bowl, cover, and refrigerate until you're ready to use. This batch yields just over half a cup.
Next, prepare the pizza dough according to your recipe instructions up to step 3. If you’re using frozen store-bought dough, ensure it’s fully thawed and rested.
Preheat your oven to 475°F (246°C). Let it preheat for a minimum of 15–20 minutes, especially if using a pizza stone. Place the stone in the oven to heat as well. Lightly grease a large pizza pan or baking sheet with 1/2 tablespoon of olive oil. Dust with cornmeal to enhance flavor and add a slight crunch to the crust.
Shape the dough by gently deflating it with your hands to release trapped air. Divide in half and store one portion for later use. On a floured surface, flatten the dough into a rough disc. Transfer it to the prepared baking pan and, with floured hands, stretch it into a 12-inch round approximately 1/2-inch thick. If the dough resists and shrinks back, allow it to rest covered for 5–10 minutes, then stretch again. Once the shape is set, pinch the edges slightly to create a rim that will hold in the toppings. If using a pizza stone, transfer the dough onto a cornmeal-dusted baker’s peel. Let the shaped dough rest briefly under a clean kitchen towel or plastic wrap.
Using your fingers, press small dimples across the surface of the dough to help prevent air bubbles. Brush the remaining olive oil across the entire surface. Spread 1/2 cup of the prepared pesto evenly over the dough, leaving a small border around the edges. Distribute the mozzarella cheese and optional tomato slices evenly over the pesto. Season lightly with a pinch of salt and freshly ground pepper.
Bake in the preheated oven for 14 to 15 minutes, or until the crust is golden and crisp around the edges. Remove from the oven and scatter chopped basil over the hot surface. If desired, garnish with a final drizzle of pesto, a sprinkle of grated parmesan, or a dash of red pepper flakes for extra heat.
Slice and serve the pizza while hot. Store any leftovers in an airtight container in the refrigerator for up to 5 days. For freezing and reheating tips, refer to the pizza dough recipe's instructions.