Heat the butter and olive oil in a large skillet over medium-low heat. Add the shallot and cook until beginning to soften, about 3 minutes. Add the garlic and cook 30 seconds. Add the shrimp, salt, red pepper flakes, and black pepper. Sauté for 3 minutes, until the shrimp are beginning to cook but are still somewhat translucent.

Add the chicken broth, lemon zest, and lemon juice. Bring to a boil and cook for 1 minute, just until the shrimp are completely opaque and cooked through. Stir in the zucchini noodles and parsley. Toss the noodles with the shrimp so that they are coated with the garlic-lemon sauce and heat just until warmed through. (Do not overcook or the zucchini noodles will become mushy.) Sprinkle with parsley and Parmesan. Serve warm.