Bring a large pot of salted water to a boil.
Cook the pasta according to package instructions until al dente.
Drain and set aside.
Season the shrimp with salt and black pepper.
Heat 2 tablespoons butter in a large skillet over medium-high heat.
Add garlic, oregano, and red pepper flakes.
Cook for 1–2 minutes until fragrant.
Add shrimp in batches and cook for 2–3 minutes, stirring occasionally, until pink and cooked through.
Remove shrimp from the skillet and set aside.
Melt the remaining 6 tablespoons butter in the same skillet.
Add the cooked pasta, arugula, and Parmesan cheese.
Toss until the greens begin to wilt, about 2 minutes.
Return the shrimp to the skillet and stir to combine.
Garnish the Garlic Butter Shrimp Pasta with fresh parsley and additional Parmesan if desired.
Serve immediately.