Pat shrimp completely dry with paper towels. Heat olive oil and 2 tablespoons butter in a large skillet over medium-high heat.
When butter foams, add shrimp in a single layer. Cook 2 minutes per side until pink and opaque. Remove to a plate and keep warm.
In the same skillet, add remaining butter and garlic. Cook 1 minute until fragrant, stirring constantly to prevent browning.
Pour in white wine and scrape up browned bits from the pan bottom. Simmer 5-6 minutes until liquid reduces by half.
Stir in lemon juice, Italian seasoning, salt, and red pepper flakes. Return shrimp to skillet with accumulated juices.
Toss everything together 2-3 minutes until shrimp are heated through and coated in sauce. Turn off heat.
Sprinkle with Parmesan cheese and parsley. Serve immediately with lemon wedges on the side.
