Preheat the oven to 425°F (220°C).
In a large baking dish, toss the quartered tomatoes, quartered onion, smashed garlic, thyme leaves, butter, and a generous pinch of salt, black pepper, and chili flakes.
Bake the vegetables for 20–30 minutes, until the tomatoes start to char and release their juices.
Carefully transfer the roasted vegetables to a blender or food processor and puree until smooth; return the puree to the baking dish and stir in the heavy cream until combined.
While the sauce bakes, bring a large pot of salted water to a boil and cook the jumbo shells until al dente according to package directions; drain and cool slightly so they can be filled.
In a medium bowl, mix the ricotta, shredded provolone, and 1/2 cup of the pesto until evenly combined.
Spoon about 1 tablespoon of the cheese mixture into each cooked shell, then arrange the filled shells in the baking dish with the tomato-cream sauce.
Drizzle the remaining 1/4 cup pesto over the shells, sprinkle the mozzarella evenly on top, and bake for about 15 minutes, until the cheese is melted and bubbly.
Remove from the oven, garnish with fresh basil, and serve warm.
