Preheat the oven to 375 degrees . In a large saucepan, melt the 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 18 minutes.
Preheat the broiler. Broil the dip until golden, 1 to 2 minutes. Serve hot with the pita chips.
