Chop sundried tomatoes and place in a small bowl. Add the onion, garlic, and capers. Pile basil leaves on top of one another and roll into a log. Thinly slice basil into green confetti and loosely combine with tomato mixture. Add oil and balsamic vinegar and a salt and cracked black pepper to the bowl and gently toss to coat. Cover and refrigerate until ready to use.
Roll out pizza dough onto a rectangular jelly roll pan or pizza pan, pressing to form to the pan.
Sprinkle dough with ½ of the grated cheese, then scatter all of the tomato mixture over the cheese. Top with remaining grated cheese and fresh mozzarella slices.
Bake until crust is golden brown and cheese is fully melted.