In a large pot or Dutch oven, melt the butter over medium heat. Once melted, add the celery and onion. Sauté for about 5 minutes, or until the vegetables are tender and the onion is translucent.
Stir in the minced garlic and cook for an additional minute until fragrant. Next, sprinkle in the all-purpose flour and stir well to combine. Cook for about 2 minutes to eliminate the raw flour taste.
Gradually add the chicken broth, stirring continuously to prevent lumps from forming. Bring the mixture to a gentle simmer, allowing it to thicken slightly.
Once the broth has thickened, stir in the chopped cooked chicken and fresh broccoli. Allow the soup to simmer for about 10 minutes or until the broccoli is tender but still vibrant green.
Reduce the heat to low and add the cream cheese to the pot, stirring until it melts and combines smoothly with the soup. Then, slowly add the shredded Mexican cheese blend, stirring until it’s fully melted and incorporated.
Finally, stir in the cooked rice. Season the soup with salt and pepper to taste. Let it heat through for a couple of minutes, and your Chicken Broccoli Cheese Soup with Rice is ready to serve!