This is a beautiful soup with a deep, rich flavor to match the color. Make sure to strain it after you puree it, a quick step that absolves you of the longer step of peeling the peppers.
Heat the olive oil over medium heat in a large, heavy soup pot and add the onion and carrot. Cook, stirring often, until the onion begins to soften, and add 1/2 teaspoon salt. Continue to cook, stirring often, until tender, about 5 minutes, and stir in the garlic and the tomato paste. Stir for a minute or two, until the garlic is fragrant and the tomato paste has darkened, and add the peppers, paprika, and another 1/2 teaspoon salt. Cook, stirring often, until the peppers begin to soften, about 5 minutes.
02Add the potatoes, stock, and bouquet garni and bring to a simmer. Add salt to taste, 1 to 2 teaspoons, cover and simmer over low heat for 1 hour. Remove the bouquet garni.
03Using an immersion blender, or in a blender or food processor fitted with the steel blade (working in batches and covering the blender lid or food processor with a kitchen towel to prevent the hot soup from splashing), blend the soup until smooth. Strain the soup through a medium strainer, pushing it through the strainer with a spatula or the bowl of a ladle, and return to the heat. Heat through, add salt and pepper to taste, and serve. Garnish with garlic croutons and slivered fresh basil or chopped thyme, and drizzle a few drops of olive oil over each serving if desired.