Preheat oven to 400°F (200°C). Line a baking sheet with aluminum foil.
Arrange the cherry tomatoes on the prepared baking sheet, drizzle with about 1 to 2 tablespoons of the olive oil, and roast for 10–15 minutes until the skins collapse and begin to brown; remove and set aside.
Wrap each ear of corn in aluminum foil (or leave in husks) and place on the baking sheet; roast alongside the tomatoes or separately for 20–25 minutes until tender. Remove and let cool slightly, then cut the kernels from the cobs with a sharp knife.
While the vegetables roast, cook the spaghetti in a large pot of salted boiling water according to package directions until al dente. Drain and rinse briefly, then return to the pot or a large bowl.
Whisk together the remaining olive oil (use the remainder of the 1/3 cup), salt, and black pepper. Toss the hot pasta with the olive oil mixture until evenly coated.
Add the grated Parmesan, chopped fresh Italian herbs, roasted cherry tomatoes, and roasted corn kernels to the pasta; toss gently to combine.
Serve immediately, optionally garnished with extra herbs or Parmesan.
