Season the chicken breasts evenly with salt and black pepper on both sides.
Heat olive oil in a large deep skillet or Dutch oven over medium-high heat.
Add the chicken breasts to the skillet and sear for 4-5 minutes on each side until golden brown. Remove chicken from skillet and set aside.
Reduce heat to medium and add minced garlic and diced onion to the same skillet. Sauté for 2-3 minutes until fragrant and translucent.
Add baby carrots and green beans to the skillet and cook for 3 minutes, stirring occasionally.
Sprinkle the flour over the vegetables and stir well to coat, cooking for 1 minute to remove raw flour taste.
Slowly pour in the chicken broth while stirring to create a sauce.
Add dried thyme, rosemary, and parsley to the skillet and stir to combine.
Return the chicken breasts to the skillet, nestling them into the vegetables and sauce.
Cover the skillet with a lid and simmer on low heat for 15 minutes, or until the chicken is cooked through and vegetables are tender.
Remove the lid and stir in the unsalted butter until melted and incorporated into the sauce.
Serve the garlic herb chicken hot with the vegetables and sauce spooned over the top.