Preheat oven to 450 degrees. Coarsely chop the onion and garlic. Heat 2 tablespoons of olive oil in a skillet over medium heat; add the onion and saute until soft, about 5 minutes. Add the garlic and cook 1 minute. Stir in the artichoke hearts together with their marinade and cook until heated through, about 7 minutes. Transfer the ingredients to a blender and puree until smooth. Add salt and pepper to taste.
Slice the red pepper into 1/8-inch round slices. Spread the artichoke puree evenly over the dough and sprinkle with mozzarella cheese. Distribute the red pepper slices decoratively over the pizza and place 2 shrimp (not cooked) inside each slice. Sprinkle with Parmesan cheese on top. Bake 25 to 30 minutes.