Heat olive oil in a skillet over medium heat.
Add shrimp, season with salt, pepper, and paprika. Cook until pink and opaque, about 2–3 minutes per side.
Remove shrimp from heat and chop coarsely if large.
Spread garlic butter on one side of each bread slice.
Place buttered side down, layer mozzarella, shrimp, cheddar, and top with the other slice of bread, buttered side up.
In a clean skillet, melt 1 tbsp butter over medium-low heat. Grill sandwich until golden brown on both sides and cheese is melted, about 3–4 minutes per side.
Sprinkle with parsley if desired. Serve hot.