Gather the ingredients.

Set an oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with foil.

Rub oil on peppers and put them under the broiler until blackened, turn to get all sides. Put into paper bag and seal.

Let rest for 15 minutes, then peel will come right off and core and seeds will fall out.

Chop peppers. Reserve one chopped pepper; set aside.

Heat oil in a stockpot over medium heat. Add onion and garlic; cook and stir until onion is translucent, about 5 minutes.

Stir in tomatoes, peppers, paprika, thyme, and sugar. Reduce the heat to medium-low and cook until tomato juices have evaporated, about 25 minutes.

Stir in broth, cayenne, hot pepper sauce, salt, and pepper; bring to a boil. Reduce the heat, partially cover, and simmer until vegetables are tender, about 25 minutes.

Place a strainer over a large bowl; pour soup into the strainer, letting liquid accumulate in the bowl. Do not clean the stockpot.

Pour solids from the strainer into a food processor or blender; purée until fairly smooth. Add purée to broth in the bowl.

Melt butter in the stockpot over medium heat. Whisk in flour and stir until mixture becomes paste-like, 1 to 2 minutes.

Gradually stir in broth-purée mixture and bring to a boil. Stir in remaining chopped peppers, reduce the heat, and simmer for 10 minutes.

Stir the soup before ladling into six bowls and topping each with 1 tablespoon of sour cream.