In a medium stockpot over medium heat, melt the butter by swirling it around occasionally to distribute it evenly around the bottom of the pot.
Add minced onion and minced garlic to the pot, and sauté until the onion and garlic are soft, which should take about 5 minutes.
Next, add crushed tomatoes, 3 ½ cups of chicken broth, cumin, chili powder, and paprika, to the pot. Stir everything together and let it simmer as you prepare the cornstarch slurry.
Create a slurry by whisking cornstarch and the remaining ½ cup of chicken broth in a small mixing bowl. Pour this mixture into the stockpot and stir to combine.
Allow the mixture to boil, then reduce the heat to medium-low and let it simmer for 5 to 10 minutes until the broth has a slightly thicker texture.
After removing the stockpot from the heat, Add heavy cream and shredded cheese to the slightly cooled stockpot. Stir well until the cheese has melted and is fully mixed in.
Stir in cream of chicken soup, green chiles, shredded chicken, white wine vinegar, chopped cilantro, and salt into the melted cheese mixture.
Once fully incorporated, let the mixture simmer for 10 minutes.
After 8 to 10 minutes, using a ladle, transfer the soup to serving bowls.
Top the soup with chopped green onions and enjoy with some tortilla chips on the side for added texture.