In a medium bowl, whisk together olive oil, parmesan*, garlic, brown sugar, soy sauce, red pepper flakes, and optional cornstarch. Add shrimp to olive oil mixture; marinate for at least 30 minutes to overnight, turning occasionally.
*Optional: leave the parmesan out of the mixture for now, and mix in at the end when mixing the sauce & pasta together.
In large pot of boiling salted water, cook pasta according to package instructions; drain well.
Heat a large skillet over medium high heat. Add shrimp and sauce mixture and cook, stirring occasionally, until pink, about 2 minutes. Stir in pasta and gently toss to combine; season with salt and pepper, to taste.
Serve immediately, garnished with Parmesan and green onions, if desired.