Preheat oven to 400°F and line a baking sheet with parchment paper. Pat shrimp dry and toss with 1 tablespoon olive oil, 1/2 teaspoon salt, and black pepper. Arrange in a single layer and roast for 8–10 minutes until pink and opaque. Bring a large pot of salted water to a boil and cook pasta until al dente, reserving 1/2 cup pasta water before draining. In the same pot, heat remaining olive oil and butter over medium heat. Add garlic and cook for 30 seconds until fragrant. Stir in lemon juice and lemon zest. Add drained pasta and toss. Gradually add reserved pasta water until the sauce becomes glossy. Stir in Parmesan cheese and remaining salt. Add roasted shrimp and toss gently. Garnish with parsley and red pepper flakes if desired. Serve immediately.