- Roast the unpeeled garlic directly on an ungreased griddle or heavy skillet over medium heat, turning occasionally, until soft (they’ll blacken in spots), about 15 minutes; cool and peel. While the garlic is roasting, toast the chiles on another side of the griddle or skillet: 1 or 2 at a time, open them flat and press down firmly on the hot surface with a spatula; when they crackle, even send up a wisp of smoke, flip them and press down to toast the other side. In a small bowl, cover the chiles with hot water and let rehydrate 30 minutes, stirring frequently to ensure even soaking. Drain and discard the water.
Combine the oregano, black pepper, cumin and 1 slice of the onion in a food processor or blender. Add the drained chiles, garlic and 1/2 cup of the broth. Blend to a smooth puree, scraping and stirring every few seconds. (If the mixture just won’t go through the blender blades, add a little more liquid.) Press through a medium-mesh strainer into a bowl.
Heat 1 tablespoon of the oil in a heavy, medium-small (2- to 3-quart) pot (such as Dutch oven or Mexican cazuela) over medium-high. When the oil is hot enough to make a drop of the puree sizzle sharply, add the puree and stir constantly until it reduces into a thick paste, 5 to 7 minutes. Stir in the remaining 1 1/2 cups broth or water, partially cover and simmer over medium-low, stirring occasionally, 20 to 30 minutes for the flavors to come together. Add the hot sauce and, if necessary, stir in a little more broth or water to bring the sauce to a medium, saucy consistency. Taste and season with about 1/2 teaspoon of the salt and the sugar.
- . In a large skillet, melt the butter with the remaining 2 tablespoons of the oil over medium-high heat. Add the shrimp and cook, stirring, for 1 minute. Add the remaining onion, breaking the rings apart, and cook, stirring, until the shrimp are done and the onion is beginning to soften, 2 to 3 minutes longer. Add the sauce and stir everything together until the sauce is boiling. Serve right away.