Make zucchini noodles using a spiralizer or julienne peeler.

Melt butter in a large skillet over medium-high heat. Pour in olive oil. Add shallot; cook and stir until tender, 4 to 5 minutes. Add minced garlic; cook until golden, about 2 minutes. Stir in wine and lemon juice; cook until sauce is reduced by almost half, about 3 minutes. Add shrimp, salt, and black pepper. Cook until shrimp turn pink, 2 to 3 minutes. Transfer shrimp to serving plate.

Stir zucchini noodles into skillet. Season with salt and black pepper. Cook until noodles are tender, 4 to 6 minutes. Return shrimp to the skillet. Stir in parsley and Parmesan cheese before serving.