Preheat oven to 500 degrees. Place a pizza stone in the oven on the center rack, if using.
Melt butter in a skillet over medium heat. When butter is melted, add leeks and sauté until tender, about 10 minutes. Season with salt, remove from heat and cool.
Sprinkle 12-inch-diameter pizza pan or baking sheet generously with cornmeal. Roll out dough on lightly floured surface to 11-inch round. Transfer to prepared pan.
Mix olive oil and garlic together in a small bowl; brush evenly over pizza dough. Add parmesan and fresh mozzarella. Top with leeks and broccolini.
Bake for 15-18 minutes. Remove from oven. Season with salt and garnish with fresh basil leaves just before serving.
