Heat 2 tablespoons of olive oil in a large Dutch oven over medium to medium-low heat.
Cut the chicken breast into bite size pieces and add to the Dutch oven. Cook chicken until it is no longer pink inside. Remove from Dutch oven and set aside.
Chop onions and mince the garlic. Add one more tablespoon of olive oil to the Dutch oven and add the onions and garlic. Cook vegetable until tender, about 10 minutes. Stirring frequently so vegetable don't burn.
Add the 3 tablespoons of flour and stir in. Gradually add the chicken broth and milk. Turn up the heat to about medium-high. Cook for about 5 minutes, the broth and milk will be slightly thickened.
Add the chicken back to the Dutch oven along with the broccoli, potatoes, and bay leaves. Bring to a boil. Turn the soup down to between medium and medium-low heat cover and cook for about 20 to 30 minutes or until potatoes and broccoli are tender.
Add the cheddar cheese and stir in until melted. Season with salt and pepper.