Pat the shrimp dry with paper towels and season with salt and pepper. Set aside.
In a large skillet, heat 1 tablespoon olive oil over medium-high heat. Add the zucchini noodles and cook for 2-3 minutes until just tender. Transfer to a plate and set aside.
In the same skillet, add the remaining olive oil and butter. Once the butter melts, add the garlic and red pepper flakes, cooking for 30 seconds until fragrant.
Add the shrimp to the skillet in a single layer and cook for 2 minutes per side until pink and opaque. Remove shrimp and set aside with the zucchini noodles.
Add the chicken broth and lemon juice to the skillet, scraping up any browned bits. Let simmer for 2 minutes until slightly reduced.
Return the shrimp and zucchini noodles to the skillet, tossing to coat in the sauce. Cook for 1 minute to heat through. Sprinkle with fresh parsley and Parmesan cheese before serving.