Set a rack in the center of the oven and preheat to 400 degrees . Slice off the top of the garlic head. Brush the cut side with 1 teaspoon olive oil. Wrap in foil and bake until tender, 40 minutes. Let cool. Squeeze the garlic cloves from their skins into a food processor. Add the mayonnaise and vinegar; puree. Transfer the aioli to a bowl and refrigerate.
Meanwhile, in a small skillet, toast the paprika, onion powder, oregano, cayenne and 1/2 teaspoon each salt and pepper over medium heat until fragrant, about 1 minute. Stir in the melted butter. Transfer to a bowl and add the shrimp to coat.
Brush a grill pan with the remaining 1 teaspoon olive oil and preheat over high heat. Add the shrimp and cook, turning once, until the spices are blackened, 2 to 4 minutes. Serve with the aioli dip.
