Rinse shrimp under cold running water, then pat completely dry on both sides using paper towels. Dry shrimp is essential for a proper sear — moisture causes steaming instead of browning.
Toss the dried shrimp in a bowl with ½ tsp Italian seasoning, ¼ tsp smoked paprika, red pepper flakes (if using), salt, and black pepper until evenly coated. Set aside.
Slice zucchini into ¼-inch half-moons, cut bell peppers into ½-inch strips, break broccoli into small florets, and halve the cherry tomatoes. Mince all 6 garlic cloves and set aside separately.
Heat 1 tbsp olive oil in a large skillet over medium-high heat. Add broccoli first for 1-2 minutes, then add bell peppers, zucchini, remaining Italian seasoning, smoked paprika, salt, and pepper. Stir-fry for 3-4 minutes until just tender, add cherry tomatoes for 1 minute, then transfer all vegetables to a plate.
Add remaining 1 tbsp olive oil to the hot skillet and arrange seasoned shrimp in a single layer. Sear undisturbed for 1-1½ minutes per side until pink, opaque, and curled into a loose C-shape, then transfer to the plate with the vegetables.
Reduce heat to medium and melt all 4 tbsp butter in the same skillet. Add minced garlic and sauté for about 1 minute, stirring constantly, until fragrant and lightly golden. Add lemon juice and lemon zest, scraping up any browned bits from the pan.
Return vegetables to the skillet and toss to coat in the sauce, then add the shrimp and toss everything together for 30-60 seconds until just heated through. Remove from heat, garnish with fresh parsley, and serve immediately with Parmesan if desired.