Step 1

Position rack in upper third of oven; preheat broiler to high.

Step 2

Place bell peppers on a baking sheet. Broil, turning every 5 minutes, until charred and softened, 15 to 20 minutes. Transfer to a bowl, cover with plastic wrap and let stand for 10 minutes. Peel, seed and chop the peppers; set aside.

Step 3

Meanwhile, melt butter in a large pot over medium-high heat. Add shallot, garlic and cumin; cook, stirring, until fragrant, about 1 minute. Add achiote paste and 1 cup broth; cook, stirring and breaking up the achiote, until it's dissolved. Add potatoes and the remaining 3 cups broth; bring to a boil. Reduce heat to maintain a simmer, cover and cook until the potatoes are easily pierced with a fork, 15 to 18 minutes.

Step 4

Puree the soup with an immersion blender or in a regular blender (in batches, if necessary) until very smooth. (Use caution when pureeing hot liquids.)

Step 5

Add the reserved peppers, milk, salt and pepper to the soup. Bring to a simmer over medium heat. Cook, stirring occasionally, until heated through, 5 to 8 minutes. Serve the soup topped with cheese, avocado and cilantro.