Preheat the oven to 350 degrees F.
Melt the butter over medium-high heat in a large skillet. Once foaming, add the shallots and cook until softened, 3 to 4 minutes. Add the garlic and cook until fragrant, 1 minute. Add the half-and-half and bring to a simmer. Whisk in the cream cheese in increments. Once incorporated and smooth, add all but 1/4 cup of the goat cheese in handfuls and whisk until melted. Remove from the heat and stir in the crabmeat and 2 tablespoons of the chopped parsley. Pour into a 1 1/2-quart casserole dish.
Mix together the panko, remaining 1/4 cup grated cheese, remaining 2 tablespoons parsley and the paprika in a small bowl. Sprinkle the top of the dip with the mixture. Bake until bubbly and hot, 20 minutes. Serve with whole wheat pita chips.