Angel Hair Pasta with Chicken

My kids aren't big on tomato sauce, so here is a vegetable-based pasta they love.

4 T. olive oil, divided
1-2 chicken breasts, cut in pieces
¾ cup sliced carrots
1 t. minced garlic
1 bag frozen broccoli florets, thawed
¾ c. chicken broth
½ c. parmesan cheese
1 lb. angel hair pasta

Heat 2 T. olive oil in skillet over medium-high. Add chicken, stirring until cooked through. Drain on paper towels and keep warm.Start water boiling for pasta.Add remaining olive oil to skillet. Cook carrots 3 minutes. Add broccoli and garlic, cook 2 more minutes.Cook pasta as directed on the package.Add broth, chicken, and cheese to vegetable mixture. Simmer on low until pasta is ready.Mix pasta and chicken-vegetable mixture together, sprinkle with freshly grated parmesan cheese and serve immediately.