Preheat the oven to 375 degrees . In a large saucepan, melt 4 tbsp. butter over medium-high heat. Add the onion and bell pepper and cook, stirring occasionally, until soft, about 7 minutes; remove from the heat. Stir in the cream cheese, 1/2 cup pecorino-romano, the paprika and mustard. Stir in the artichoke hearts and shrimp; season with salt and pepper.
Transfer the mixture to a 9-by-13-inch baking dish and top with the remaining 1/2 cup pecorino-romano. Bake until warmed through, about 20 minutes.
Butter the outsides of the bread slices and place a scoop of dip between 2 slices; grill until golden-brown on both sides.