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Step 1
Season the chicken pieces all over with salt and pepper. Heat oil in a large frying pan over medium-high heat. Add chicken and cook, undisturbed, until brown on one side, flip and repeat on the other side, about 10 minutes total. Transfer with tongs to the Crock Pot.
Step 2
Add onion, poblanos, bell pepper, and garlic to the pan and season with salt and pepper. Cook, stirring occasionally, until tender and starting to brown, about 10 minutes. Scrape into the Crock Pot with the chicken.
Step 3
Add tomatoes (with their juices), spices, and chicken broth to the Crock Pot and cook on high for 4 hours or low for 8.
Step 4
About 30 minutes before serving, remove chicken pieces from the Crock Pot. Remove any skin and bone and shred meat into bite-sized pieces. Return chicken to the Crock Pot. Add the half-and-half, and sour cream and stir to combine. Taste and add more salt as needed. Return soup to a simmer.
Step 5
While you are waiting for the soup to come back to a simmer. Heat the oven to 400°F. Toss the tortilla strips and oil on a baking sheet. Spread into an even layer and bake until crisp, about 10 minutes, tossing occasionally. Sprinkle with salt.
Step 6
Serve the soup with a generous helping of tortilla strips, some chopped cilantro, and hunks of avocado, and a few slices of jalapeño if desired.