Prep the shrimp and zucchini: Pat the shrimp dry with paper towels and season with salt, pepper, and paprika. Slice the zucchini into half-moons so they cook evenly and keep some bite.
Warm the skillet: Heat a large skillet over medium-high. Add 1 tablespoon olive oil.
When it shimmers, add half the shrimp in a single layer. Cook 1–2 minutes per side until just pink. Remove to a plate.
Repeat with the remaining shrimp and another tablespoon of oil.
Sauté the zucchini: Lower heat to medium. Add 1 tablespoon butter to the skillet. Stir in the zucchini, a pinch of salt, and Italian seasoning.
Cook 3–4 minutes, stirring occasionally, until the edges start to brown but the centers are still firm.
Build the garlic butter: Push the zucchini to the sides of the pan. Add the remaining 2 tablespoons butter to the center, then the minced garlic and red pepper flakes. Stir 30 seconds, just until fragrant.
If using, splash in a couple tablespoons of white wine and let it sizzle for 20–30 seconds.
Bring it together: Return the shrimp and any juices to the skillet. Add lemon zest and lemon juice. Toss everything to coat in the butter sauce.
Cook 1 minute more, just to warm the shrimp through.
Finish and serve: Taste and adjust salt, pepper, and lemon. Sprinkle with parsley (and Parmesan if using). Serve right away with crusty bread, rice, zucchini noodles, or over cooked pasta.