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Step 1
Heat medium stockpot over medium heat. When stockpot is hot, add butter to pot. Heat butter, swirling pot occasionally to distribute butter evenly around bottom of pot, until butter is melted.
Step 2
Add minced onion and minced garlic to pot with melted butter. Sauté until onion and garlic have softened, approximately 5 minutes.
Step 3
Once onion and garlic are soft, add chili powder, paprika, cumin, crushed tomatoes, and 3 ½ cups chicken broth to stockpot. Stir to incorporate ingredients. Let mixture simmer while preparing cornstarch slurry.
Step 4
Add cornstarch and remaining ½ cup chicken broth to small mixing bowl. Whisk until fully incorporated, then pour slurry mixture into stockpot. Stir to incorporate.
Step 5
Increase heat under stockpot to medium-high. Bring mixture to boil, then reduce heat to medium-low and simmer 5 to 10 minutes, or until broth is slightly thickened.
Step 6
Move stockpot to cool stovetop burner. Let mixture cool slightly, then add heavy cream and shredded cheese. Stir until heavy cream is incorporated and shredded cheese has melted.
Step 7
Once cheese has melted, return stockpot to heat. Add cream of chicken soup, shredded chicken, green chiles, chopped cilantro, white wine vinegar, and salt. Stir until ingredients are fully incorporated, then let mixture simmer 10 minutes.
Step 8
After 10 minutes, ladle soup into serving bowls. Top with chopped green onions and serve warm with tortilla chips if desired.