Preheat the oven to 375°F. Roll the pie crust into a 9-inch pie dish and crimp the edges as desired. Line with parchment paper and pie weights or dried beans. Bake for 10 minutes, then remove the weights and bake for another 5 minutes until lightly golden. Set aside.
Increase the oven temperature to 400°F. Add the halved cherry tomatoes to a baking sheet and toss with olive oil, Italian seasoning, salt, and black pepper. Roast for 18–22 minutes until lightly caramelized and some moisture has cooked off. Let cool slightly. In a large mixing bowl, whisk together the eggs, heavy cream, whole milk, shallot, grated garlic, Italian seasoning, salt, and black pepper until smooth.
Sprinkle the parmesan cheese evenly into the bottom of the blind baked crust. Add the mozzarella, roasted tomatoes, and chopped basil evenly throughout the crust, reserving a few tomatoes for the top if desired. Slowly pour the custard mixture over the filling.
Bake at 375°F for 50–60 minutes or until the edges are fully set and the center has only a slight wobble. The center should no longer look wet or liquidy. If the crust begins browning too quickly, loosely tent the edges with foil (I added foil for the last 10-15 minutes).
Let the quiche rest for at least 15 minutes before slicing. Top with balsamic glaze and fresh basil ribbons if desired.