Adjust an oven rack 4- 6 inches below the heater element; preheat the broiler.

Line a baking sheet with foil and broil the bell peppers until blackened all over, watching closely and turning often, about 10 minutes.

Remove from the oven and pull up the foil edges to make a sealed packet. Let peppers steam for 10 minutes. Peel off the skin of the peppers, remove the seeds and tear into chunks. Set aside.

While peppers roast, heat a large skillet over medium heat. Add dried chiles and cook, turning often to prevent burning, until fragrant (they shouldn’t darken much), about 2 minutes.

When cool enough to handle, stem and seed the chiles, tear into pieces and add to a food processor along with the hot water. Blend until peppers are pureed and mostly smooth, 2- 3 minutes.

Pass chile puree through a mesh strainer to remove any tough bits of skin, and set aside. Rinse the food processor bowl and set aside.

Heat 2 tablespoons of olive oil in the same skillet over medium-low heat. Add the torn bread and fry, flipping every so often, until all the sides are deeply golden brown, about 10 minutes total.

When bread is just about done, add almonds to the pan. Cook for 3- 4 minutes, stirring often, until toasted and nutty smelling. Transfer to the food processor.

Heat another 1 tablespoon olive oil in the skillet and add the tomato paste. Cook over medium-low heat, stirring, as the paste sizzles and darkens, about 2- 3 minutes. Scrape into the food processor. Add tomato puree, garlic, paprika, cayenne, vinegar, and salt and pulse until coarsely ground.

Add roasted peppers and chile puree and blend until mostly smooth, about 1 minute. With the machine running, slowly pour in 1 cup olive oil until smooth and combined (don’t worry if it separates, that’s normal). Transfer to a bowl. Taste and add more salt or vinegar, if needed.