Combine the seasonings—chili powder, mustard powder, garlic powder, onion powder, cumin, cinnamon, and cayenne—and set them aside. Allow your cream cheese to soften at room temperature while you shred your cheeses from blocks.
In a large soup pot over medium heat, melt butter together with olive oil. Once heated, add diced onions and jalapeno peppers. Soften them for about four minutes until fragrant and translucent before adding minced garlic for another minute of cooking.
Pat your chicken dry and season both sides generously with salt and pepper. Add it to the pot along with all remaining ingredients except for the cream cheese and shredded cheeses.
Bring your mixture to a gentle boil and allow it to cook through slowly for about 15–20 minutes. Afterward, remove the chicken from the pot and shred it using two forks before returning it back into the broth.
Reduce heat to low and stir in softened cream cheese until fully combined. Follow by adding shredded cheddar and Monterey Jack cheeses until they melt completely.
Give your soup a taste test! Adjust seasonings as needed before serving up bowls brimming with warmth and flavor.