Pat the shrimp dry and season lightly with salt and black pepper. Set aside while you prepare the rest of the ingredients.
Heat the butter and olive oil together in a large skillet over medium heat until the butter melts. Add the minced garlic and red pepper flakes and cook for about 30 seconds until fragrant.
Add the shrimp to the skillet in a single layer. Cook for 2 minutes per side until they turn pink and opaque. Remove the shrimp to a plate and set aside.
Pour the white wine or broth into the same skillet and stir to loosen any browned bits. Add the lemon juice and zest, then let the sauce simmer for 1 minute.
Add the spiralized zucchini noodles to the skillet and toss gently for 1 to 2 minutes until just warmed through but still firm. Return the shrimp to the pan and stir to combine.
Remove the skillet from the heat. Sprinkle with chopped parsley and grated Parmesan cheese before serving.