Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1/2 cup cooking water, then drain.
Meanwhile, melt the butter in a large nonstick skillet over medium heat. Add the carrots, bell peppers, squash, chile, garlic, thyme and vinegar; season with 1/2 teaspoon salt and a few grinds of pepper. Reduce the heat to medium low; cover and cook, stirring halfway through, until the vegetables are very tender, about 20 minutes.
Add the heavy cream to the skillet; bring to a simmer. Gradually stir in the parmesan until just melted, about 1 minute. Add the tomatoes.
Increase the heat to medium and add the pasta and the reserved cooking water. Cook, tossing, until coated, about 2 minutes; season with salt and pepper. Top with more parmesan.