Measure the oil into a large skillet and set over medium heat. When hot, oil-toast the chiles 1 or 2 pieces at a time until very toasty smelling and blistered, only a few seconds per side. Pour off all but a generous film of oil from the skillet and set aside. Transfer the chiles to a large bowl and measure in 4 cups hot tap water; a small plate on top will keep the chiles submerged. Let rehydrate for about 20 minutes.
Measure the garlic, oregano, black pepper, cumin, cloves and vinegar into a blender or food processor. Pour in the rehydrated chiles, liquid and all (do this in two batches if necessary). Process the mixture to a smooth puree. Press through a medium-mesh strainer set over a bowl.
Set the chile-frying skillet over medium heat. When quite hot, add the adobo and stir until reduced to the thickness of tomato paste, about 10 minutes. Stir in the broth, reduce the heat to medium-low and simmer for 30 minutes or so. The finished sauce should be quite light in texture, not watery, but just one stage thicker. (A good test is to pour a little on a plate and watch it spread: If it flows evenly, it’s right; if it doesn’t flow much and water begins separating around the edges, it’s too thick.) Season with salt (usually about 1 tablespoon) and sugar—it should be a little sweet-sour with a hint of saltiness. Serve warm.