Spiralize the zucchini into noodles and set them on paper towels. Peel and devein the shrimp if needed, then pat them very dry. Slice 2 garlic cloves and mince the rest.

Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Season the shrimp with salt and pepper and add them in a single layer. Cook 1 to 2 minutes per side until pink, then move them to a plate.

Lower the heat to medium. Add 1 tablespoon of butter, the sliced and minced garlic, and the red pepper flakes. Cook 1 minute, stirring, until fragrant and just golden.

Pour in the chicken broth and lemon juice and simmer 1 minute, scraping up the browned bits.

Add the zucchini noodles and toss for about 2 minutes, just until barely tender.

Return the shrimp to the pan, take the skillet off the heat, and stir in the remaining 2 tablespoons of butter until the sauce turns glossy. Top with parmesan and parsley and serve right away.