Prep the shrimp: Pat the shrimp dry with paper towels and season lightly with salt and pepper.
Dry shrimp sear better and release less water into the sauce.
Build the base: Add butter, olive oil, minced garlic, Italian seasoning, red pepper flakes (if using), and broth to the slow cooker. Cover and cook on Low for 1 hour. This gives the garlic time to mellow and the flavors to bloom.
Add cream and Parmesan: Stir in the heavy cream and 1/2 cup Parmesan.
Cover and cook on Low for another 30 minutes so the sauce comes together and slightly thickens.
Cook the shrimp: Nestle the shrimp into the sauce in an even layer. Cover and cook on Low for 15–25 minutes, until the shrimp are opaque and just curled into a loose “C.” Do not overcook.
Finish with lemon: Stir in lemon zest and juice. Taste and adjust salt and pepper.
Add more Parmesan if you want a thicker, cheesier finish.
Serve: Spoon the shrimp and sauce over hot pasta or rice, or with toasted bread for dipping. Sprinkle with parsley and extra Parmesan right before serving.