Melt butter in the skillet, then sauté chopped onions and carrots over medium-low heat for 5 minutes until softened. Stir in frozen peas, corn, thyme, rosemary, and garlic powder.
Sprinkle the flour over the sautéed vegetables and stir until evenly coated. Pour in the chicken broth and bring to a gentle simmer while stirring to combine and avoid lumps. Add the whole milk.
Return the chicken to the skillet and simmer on low heat for 8 to 10 minutes until the sauce thickens and the chicken is cooked. If too thick, add more broth to thin it.