Cook pasta in a large pot of salted boiling water according to package instructions until al dente. Reserve 2 cups of pasta water, then drain and set aside.
Season shrimp with salt and pepper.
In a large skillet over medium-high heat, melt butter. Add shrimp in a single layer and cook for about 30 seconds per side until pink and opaque. Transfer shrimp to a plate and set aside.
In the same skillet, reduce heat to low and add more butter if needed. Add grated garlic and crushed red pepper flakes, warming gently until fragrant, about 20-30 seconds.
Pour in heavy cream, season with salt and pepper, and let simmer for 3-4 minutes until steaming and slightly thickened.
Add cooked pasta and shrimp back to the skillet. Stir in shredded Parmesan cheese until melted and creamy.
If the sauce is too thick, add reserved pasta water a little at a time until you reach desired consistency.
Garnish with dried oregano or fresh parsley and serve immediately with lemon wedges.
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Notes
Store leftovers in airtight containers in the refrigerator for up to 3 days. Reheat gently on the stove with a splash of water or cream.