In a large pot or Dutch oven, heat olive oil over medium heat. Add diced chicken and cook until browned on all sides, about 5-7 minutes. Remove the chicken and set aside. In the same pot, add chopped onion and cook until translucent, approximately 3 minutes. Stir in minced garlic and cook for an additional minute until fragrant.

Add broccoli florets to the pot, cooking for 3-4 minutes until they become vibrant green. This step ensures the broccoli retains its color and nutrients.

Sprinkle flour over the vegetables, stirring continuously for about 2 minutes to eliminate the raw flour taste. Slowly whisk in chicken broth, ensuring a smooth consistency. Return the cooked chicken to the pot. Bring the mixture to a gentle simmer and cook for 10 minutes, allowing flavors to meld.

Reduce the heat to low. Gradually stir in milk, ensuring it integrates seamlessly without curdling. Add shredded cheddar cheese in small batches, stirring until fully melted and the soup achieves a creamy texture. Season with salt, freshly ground black pepper, and red pepper flakes if desired. Let the soup simmer for an additional 5 minutes to enhance the flavors.