Start by cleaning and deveining the shrimp if not already done. Pat them dry with paper towels to remove excess moisture. Season lightly with salt and pepper for a balanced flavor base.
Heat olive oil and butter in a skillet over medium heat. Add shrimp and cook for about 2–3 minutes per side until pink and opaque. Remove them from the pan and set aside to avoid overcooking.
In the same skillet, sauté minced garlic until fragrant, about 1 minute. Pour in heavy cream and stir gently, letting it simmer slightly. Add cream cheese and Parmesan, stirring until smooth and creamy.
Return the cooked shrimp to the skillet and coat them well in the sauce. Sprinkle Italian seasoning and adjust salt and pepper to taste. Let everything simmer briefly so flavors blend together.
Lay tortillas flat and spoon the creamy shrimp mixture evenly across each one. Sprinkle mozzarella cheese on top for extra richness. Roll them tightly and place seam-side down in a baking dish.
Preheat your oven and bake the roll-ups until the cheese melts and the tops turn lightly golden. This step helps everything hold together and enhances the flavor.
Remove from the oven and let them rest for a few minutes. Garnish with fresh parsley for a pop of color and freshness. Serve warm for the best taste and texture.