• Chopped fresh basil and chives
Divide pizza dough in half. Roll each into a ball. Let stand covered with a towel on a well-floured work surface.
Meanwhile, heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add onion. Cook, stirring until onions are golden and soft, about 10 minutes. Sprinkle with sugar; cook to caramelize, about 2 minutes. Transfer to a plate. Add sliced mushrooms and 1 tablespoon olive oil to skillet. Cook, stirring, until mushrooms are golden, about 6 minutes. Stir in garlic; cook, 1 minute. Remove from heat. Stir in onions and thyme. Let cool.
Put a pizza stone or a heavy-duty baking sheet on the middle oven rack. Preheat oven to 550 degrees. Have all ingredients nearby. Sprinkle a baking sheet or a peel with cornmeal.
Put 1 dough ball on a floured surface. Use a floured rolling pin to gently roll the dough ball into a 12-inch round. Place on prepared baking sheet or peel.