1. Preheat the oven to 425°. In a large bowl, toss the chicken wings with 2 tablespoons of the oil and a generous pinch each of salt and pepper. Arrange the chicken wings in a single layer on a large nonstick baking sheet and bake for about 40 minutes, or until golden and crusty. Carefully pour off the fat from the baking sheet.
2. Meanwhile, arrange the tomatoes, cut side up, in a large baking dish and drizzle evenly with 1 tablespoon of the oil. Season the tomatoes with salt and pepper and roast for 20 minutes, or until softened and lightly browned on the bottom. Transfer the tomatoes and their juices to a blender or food processor and pulse several times until smooth. Add the goat cheese and the remaining 2 tablespoons of oil and process until smooth. Season the sauce with salt and pepper.
3. Preheat the broiler. Transfer the chicken wings to a large bowl and toss with half the tomato sauce. Spread the wings in a single layer on the baking sheet and broil for 5 minutes, rotating the pan as necessary, until evenly browned and crisp. Transfer the hot chicken wings to a serving platter. Pour the remaining tomato sauce into a bowl and pass at the table for dipping.
Make Ahead: The recipe can be prepared through Step 2 and refrigerated overnight. Rewarm the chicken wings in the oven before broiling.