Preheat the broiler to its highest temperature. Slice each tomato in half and arrange cut side up on a baking sheet.
Place the pan on a rack as close to the broiler as possible and cook for 30 to 40 minutes until nicely blackened.
Meanwhile, place the dried chiles in a bowl with the tomato vines and cover with 2 cups boiling water. Set aside.
Mix the lime zest with the sour cream and season with salt and pepper. Refrigerate until needed.
When the tomatoes are ready, carefully turn them over and broil for another 5 minutes, or until the skins are crisp and charred. This may happen quickly so keep a watchful eye.
When ready, discard the vines and transfer the tomatoes and all of their juices into a blender along with the chiles, their soaking water, and lime juice. Blend until smooth, season to taste, reheat, and serve garnished with a spoonful of citrus sour cream.