Preheat oven to 400°. Cut your chicken breasts in half lengthwise and set aside.
Mix together garlic powder, salt, smoked paprika, and black pepper in a small bowl. Divide the seasoning mixture in half, then season all sides of your 4 pieces of chicken breast evenly using half of your seasoning mixture. Reserve the other half of the seasoning mixture for step 5.
Heat 2 tbsp of oil in your dutch oven on medium, then add your chicken breasts to the pot. Cook about 3-4 minutes on each side until browned. Remove from pot and set aside.
Add the remaining 1 tbsp of oil to the Dutch oven and heat on medium. Add the carrots, mushrooms, and onion, and ¼ cup chicken broth to the pot. Scrape up any brown bits on the bottom of the Dutch oven, and cook the vegetables for 7-8 minutes, stirring occasionally.
Meanwhile, whisk together the remaining 1 cup chicken broth, flour, remaining seasoning, and Dijon mustard until no clumps remain and pour over the vegetables. Add the half n half as well, stir, and bring to a boil.
Once boiling, turn off the heat and nestle the chicken into the liquid and vegetables so the chicken breasts are mostly submerged in the liquid. Sprinkle with fresh thyme leaves, then cover and bake for 10-12 minutes, or until the chicken reaches an internal temperature of 165°. Serve!