Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
Heat olive oil in a large skillet over medium-high heat. Add crushed garlic, and cook for a few seconds until it turns golden brown. Stir in the squid, and cook until it turns white. Pour in white wine and cherry pepper slices; bring to a simmer, and cook until the wine is reduced by half, about 3 minutes.
Stir cornstarch into the cream, and add to the simmering calamari. Season with red pepper flakes, basil, salt, and pepper; stir until thickened. To serve, toss pasta with sauce, and sprinkle with Parmesan cheese.