In a large pot of boiling salted water, cook pasta, stirring occasionally, until al dente according to package directions. Drain.
Meanwhile, in a large skillet over medium heat, melt 1 Tbsp. butter with oil. Add shrimp; season with salt and black pepper. Cook, flipping halfway through, until pink, about 2 minutes per side. Transfer to a plate.
In same skillet over medium heat, melt remaining 3Tbsp. butter. Add garlic and cook, stirring, until fragrant, about 1 minute. Add wine, lemon juice, and red pepper flakes and bring to a simmer. Cook, stirring, until liquid is slightly reduced, about 2minutes. Add Parmesan and cook, stirring, until melted, about 2 minutes more
Return shrimp to skillet along with parsley and cook, stirring, until warmed through, about 1 minute. Add pasta and toss to combine.
Divide pasta among bowls. Top with Parmesan.