Preheat oven to 400 degrees F. For roasted tomatoes: Line a 15x10x1-inch baking pan with parchment paper. Place tomato quarters on parchment paper. In a small bowl, combine 2 tablespoons of the olive oil and 2 cloves of the minced garlic. Brush both cut sides of quarters with oil mixture. Roast for 20 to 25 minutes or until tomatoes are soft and beginning to brown. Remove from oven; cool tomatoes in pan on a wire rack.
In a large skillet, cook and stir the onions in the remaining 2 tablespoons olive oil over medium to medium-high heat for 8 to 10 minutes or until tender. Reduce heat to medium-low. Stir in the remaining 2 cloves of minced garlic. Cook, stirring occasionally, about 10 minutes more or until onions are very soft and caramelized. With a potato masher or fork, mash onion mixture. Season to taste with salt and black pepper.
On a lightly floured surface, roll pizza dough into a 10-inch circle. Place in a greased 11-inch tart pan with a removable bottom; press dough onto bottom and up the sides. Prick dough with a fork; brush with beaten egg. Bake for 12 to 15 minutes or until crust is golden brown. Remove from oven.
Evenly spread mashed onion mixture onto crust. Top with roasted tomatoes and mozzarella; drizzle with additional olive oil.
Bake for 10 to 15 minutes or until cheese melts. Top with basil leaves. Cut into wedges to serve. Serve warm. Makes 6 servings.