Preheat the oven to 325 degrees F.
Halve the tomatoes lengthwise and arrange them cut-side up on wire racks set over rimmed baking sheets. Drizzle with EVOO and sprinkle with the thyme, salt and pepper. Roast until the tomatoes are slumped but still moist in the center, about 1 hour 15 minutes. Let cool.
Heat 2 tablespoons EVOO in a pot over medium heat. Add the garlic and onions, and season with salt and pepper. Cook until very soft but not caramelized, 12 to 15 minutes. Add the vodka and cook until reduced by half. Add the chicken stock and roasted tomatoes and heat through. Stir in the mascarpone, then puree into a fairly smooth, creamy sauce using an immersion blender, food processor or blender. Return the sauce to the pot, add the basil and stir until wilted.
Bring a large pot of water to a boil for the pasta, and season with salt. Add the pasta and cook until al dente. Drain.
Toss the pasta with the sauce and transfer to a glass or ceramic baking dish. Top with the mozzarella and parmesan. If you are making the pasta ahead of time, cool it and then cover with parchment and foil. Store in the refrigerator.
When you are ready to serve, preheat the oven to 375 degrees F.
Bake the casserole, covered, until heated through, about 45 minutes. Uncover and bake until brown and bubbly on top, 15 to 20 more minutes.
Cook's Note: Serve with a salad of escarole or romaine dressed with lemon juice, EVOO, salt and pepper.