Heat medium stockpot over medium heat. When stockpot is hot, add 2 tablespoons butter to pot. Heat butter, swirling pot occasionally to distribute butter evenly around bottom of pot, until butter is melted.

Add ½ cup minced yellow onion and 2 teaspoons minced garlic to pot with melted butter. Sauté until onion and garlic have softened, approximately 5 minutes.

Once onion and garlic are soft, add 1 teaspoon chili powder, ½ teaspoon paprika, 1 teaspoon cumin, 1 14.5-ounce can crushed tomatoes, and 3 ½ cups chicken broth to stockpot. Stir to incorporate ingredients. Let mixture simmer while preparing cornstarch slurry.

Add ½ cup chicken broth and ¼ cup cornstarch to small mixing bowl. Whisk until fully incorporated, then pour slurry mixture into stockpot. Stir to incorporate.

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.

Move stockpot to cool stovetop burner. Let mixture cool slightly, then add 1 cup heavy cream and 1 cup shredded Mexican-style cheese blend. Stir until heavy cream is incorporated and shredded cheese has melted.

Once cheese has melted, return stockpot to heat. Add 1 10.5-ounce can cream of chicken condensed soup, 1 cup shredded rotisserie chicken, 1 4-ounce can chopped green chiles, ½ tablespoon chopped cilantro, 1 tablespoon white wine vinegar, and 1 teaspoon salt. Stir until ingredients are fully incorporated, then let mixture simmer 10 minutes.

After 10 minutes, ladle soup into serving bowls. Top with chopped green onions and serve warm with white corn tortilla chips if desired.