Chef Jeff's Chile Relleno Soup

Ingredients

• 2 (7 oz.) cans diced green chiles
• 2 tbsp. butter
• ½ small onion, diced
• 1 tbsp. minced garlic
• 1 tsp. cumin
• 1 quart chicken broth
• 1 tsp. kosher salt + ½ tsp. pepper
• 1 ½ lbs. boneless chicken thighs
• 8 oz. cream cheese
• 1 ½ cup shredded Oaxaca cheese
• 8 slices pepperjack cheese
• Canola oil as needed