Place the spiralized zucchini on a paper towel-lined tray and sprinkle with a pinch of salt to draw out moisture; let sit for 10 minutes then pat dry.
Season the raw shrimp with kosher salt and black pepper.
In a large skillet, heat the olive oil and butter over medium-high heat until the butter is melted and foaming.
Add the shrimp to the skillet in a single layer and sear for 1.5 to 2 minutes per side until opaque and pink. Remove shrimp from the pan and set aside on a plate.
In the same skillet, add the minced garlic and red pepper flakes, sautéing for 60 seconds until fragrant but not browned.
Pour in the white wine or chicken broth to deglaze the pan, scraping the bottom with a wooden spoon, and simmer for 2 minutes until the liquid reduces by half.
Increase heat to high, add the zoodles to the skillet, and toss constantly for 2 to 3 minutes until just tender.
Return the cooked shrimp and any accumulated juices to the skillet.
Add the lemon juice and fresh parsley, tossing all ingredients for 1 minute to incorporate the sauce.
Remove from heat, garnish with grated Parmesan cheese, and serve immediately to prevent zoodles from becoming watery.