Bring a large pot of well-salted water to a boil.
Combine the shrimp, grated garlic, 2 Tbs. of the olive oil, and 1 tsp. kosher salt in a large bowl and toss to combine; set aside.
Add the pasta to the boiling water, stir well and cook according to package directions until al dente. Reserve ½ cup of pasta cooking water and drain the pasta.
In a large skillet, melt 2 Tbs. of the butter with the remaining 1 Tbs. olive oil over medium heat. Add the sliced garlic, red pepper flakes, and lemon peel and cook, stirring often, until fragrant, about 1 minute. Add the wine, lemon juice, ¼ cup of the reserved pasta water, salt and pepper and bring to a simmer, and let reduce by half, about 2 minutes.
Reduce the heat to medium-low and stir in the remaining 2 Tbs. butter until blended. Add the shrimp and cook, stirring often until they just turn pink, 2 to 4 minutes depending upon their size.
Add the pasta, parsley, and more reserved pasta cooking water if needed, to the pan. Toss it all together and serve right away.