Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs. Reserve 1 cup of the cooking water; drain the pasta.
Meanwhile, heat a grill pan over high heat. Stuff the garlic slices into the cut sides of each tomato, then sprinkle with the red pepper flakes, and salt to taste; drizzle with 2 tablespoons olive oil. Grill the tomatoes and pepper strips, skin-side down, until charred and tender, about 10 minutes; transfer to a cutting board.
Brush the zucchini and eggplant slices lightly with olive oil; season with salt. Grill until marked and tender, about 5 minutes per side. Roughly chop the tomatoes and transfer to a large pot; cook over medium-high heat, 3 minutes. Roughly chop the remaining grilled vegetables and add to the pot along with the herbs and the remaining olive oil.
Add the pasta to the pot and cook, tossing, until heated through, 2 to 3 minutes. Add some of the reserved pasta water to loosen, if needed. Divide among bowls; top with the goat cheese and more herbs.