Place the peaches, tomatoes, onion, kidney beans, bocconcini and 5 cloves of the garlic in a large bowl and set aside.
In a small bowl, whisk to combine the garlic, balsamic vinegar, 2 tbsp of the olive oil and the crushed red pepper flakes. Pour the mixture over the peaches, tomatoes, etc. and add the basil and fresh ground pepper. Toss to coat. Taste and season with salt accordingly.
Cover the mixture and transfer to the fridge. Let sit for at least 1 hour or overnight. Take the mixture out of the fridge 30 minutes prior to serving. This will take the chill off of the sauce.
Place a large pot of water over high heat and bring to a boil. Liberally salt the water and add the pasta. Cook according to the package's directions. Reserve a cup of the pasta water, then drain and rinse the pasta and set aside.
In a large deep skillet, heat the remaining olive oil over medium heat until shimmering. Add the last clove of garlic and saute until fragrant. Add the pasta, butter, and Parmigiano-Reggiano to the pan. While stirring constantly, add as much of the pasta water as you need to form a thin, glossy sauce. Take the pasta off of the heat once all the shells are coated. Finish the pasta with fresh ground pepper.
Divide the pasta among six bowls or plates. Spoon the bruschetta over top, sprinkle with additional Parmigiano-Reggiano and tuck in.