Make dough: Whisk together flour and salt in a bowl. With a pastry blender or 2 knives, cut in butter and mozzarella until size of peas. Sprinkle 1 Tbsp. ice water on top, stirring with a fork to moisten evenly. Add water just until dough comes together when pressed. Pat dough together to form a ball and knead lightly. Flatten ball into a disk, wrap in wax paper and refrigerate for at least 30 minutes or up to 2 days.
On a floured surface, using a floured rolling pin, roll out dough into an 11-inch round. Ease into a 9-inch fluted tart pan with a removable bottom. Fold in overhang and press dough against side of pan so it extends 1/8 inch above rim. Line with parchment paper and refrigerate until firm, at least 15 minutes.
Preheat oven to 425°F. Fill shell with pie weights and bake for 15 minutes. Remove parchment paper and weights and bake for 5 minutes longer. Let pan cool on a rack.
Make filling: In a large nonstick skillet, heat oil over medium heat. Add onion and cook until soft, about 5 minutes. Add plum tomatoes, tomato paste, salt and pepper; cook, stirring, until thick, 15 to 20 minutes. Stir in basil. Transfer to a bowl and let cool to room temperature, about 25 minutes.
Spread tomato mixture on crust and top with sliced tomatoes. Bake for 30 minutes. Remove side of pan, garnish with basil and serve.