Quick Chicken with Gouda Gravy and Smashed Brocco-tatoes

Chicken breast, skinless boneless

Baking potatoes

Chicken broth

Flour

Pepper

Salt

Olive oil, extra-virgin

Butter

Gouda cheese

Milk or half-and-half

head Broccolicut into 1-inch florets, stalks peeled and cut into 1/2-inch cubes

2 tablespoons fresh thyme or 1 teaspoon dried