Heat a medium skillet over high heat. Add the cored tomatoes and cook until they are charred on all sides, about 5 minutes. Remove to the bowl of a food processor fitted with the metal blade.
Let the skillet cool slightly by taking it off the heat or decreasing the heat, depending on how smoking-hot your skillet is. Have the heat at low and add the oil (the skillet will still hold a great deal of heat). Add the onion and garlic, and saute, stirring occasionally, until both are a deep golden-brown, 8 to 10 minutes. Remove from the heat and let them cool slightly. Transfer to the food processor bowl containing the reserved charred tomato, and process until smooth. Transfer the mixture to a large saucepan. Cook over medium-low heat until thickened, 5 to 7 minutes. Season with salt and pepper.
Add the chopped collards and cook until just tender, 15 to 20 minutes. Taste and adjust for seasoning with salt and pepper. Serve warm.