Preheat the oven to 450 degrees F.

Cut top 1/2-inch off tomatoes and reserve. Remove seeds, juice and pulp from tomatoes, leaving 1/2-inch thick shells. Finely chop tomato tops. Lightly salt the insides of the tomatoes. Let the tomatoes rest, cut sides down, on a plate lined with paper towels until ready to assemble and bake.

In a skillet, heat the oil over medium heat. Add the onions and cook, stirring, until softened, about 5 minutes. Add the garlic and cook, stirring, until fragrant, 30 seconds. Add the chopped tomato tops, zucchini and squash. Saute until the vegetables just soften and most of juice has evaporated, about 3 minutes. Stir in 1 teaspoon basil and the thyme. Season, to taste, with salt and freshly ground black pepper. Remove from the heat and let cool slightly.

Place the tomato shells in an oiled baking dish. Spoon the vegetable mixture into the tomatoes, allowing any extra to spill over into the pan. Sprinkle the top of each tomato with 1 tablespoon of cheese. Bake on the upper rack of the oven until heated through, the tomatoes are tender, and the cheese begins to turn golden brown, about 10 minutes.

Remove from the oven and garnish each with 1/2 teaspoon of the remaining basil. Serve hot.