Pour the drained tomatoes into a blender or food processor. Add the chipotle chiles, chipotle canning sauce and black garlic (if you are using it). Process until smooth.
In a very large (12-inch skillet), heat the oil over medium. Add the raw garlic (if you are using it) and stir until fragrant and golden, about 1 minute. Pour in the tomato mixture. Cook, stirring frequently, for 5 minutes for the flavors to meld. Add enough broth or water to achieve a light tomato sauce consistency. Taste and season highly with salt, usually about 1 teaspoon.
Add the shrimp to the pan. Cook, stirring nearly constantly, until the shrimp are cooked through, about 4 minutes. Stir in a little more broth or water if the sauce has thickened too much. Scoop onto dinner plates and sprinkle with the cilantro.