Bring a large pot of salted water to a boil. Cook the pasta al dente according to the package directions. Drain and add to a large mixing bowl. Drizzle with 1 tablespoon of the olive oil to prevent the pasta from sticking and let cool to room temperature.
Meanwhile, heat ½ tablespoon of olive oil in a large skillet over medium-high heat. When the oil is hot and shimmering, add the corn to the pan and season with a little bit of salt and pepper. Cook for 4 to 5 minutes, or until the corn is bright yellow and lightly browned in spots. Transfer the corn to a bowl and let cool to room temperature.
Add the cooled corn, roasted red peppers, arugula, basil, and crushed red pepper (if using) to the bowl with the pasta. Drizzle with the remaining 1½ tablespoons of olive oil and the vinegar and toss to combine. Add half of the goat cheese and gently toss again. Taste and season with a little extra salt and pepper if needed. (You can also add a little bit more oil and balsamic if you like.)
Serve immediately topped with the remaining goat cheese.