Cook Chicken: Heat olive oil in a large skillet over medium heat. Season the chicken pieces with salt and pepper. Add the chicken to the skillet and cook until golden brown and cooked through, about 5-7 minutes. Remove chicken from the skillet and set aside.
Sauté Vegetables: In the same skillet, melt butter over medium heat. Add garlic, onion, and red bell pepper. Cook, stirring frequently, until onions are translucent and peppers are tender, about 3-4 minutes. Stir in thyme and basil.
Make the Sauce: Sprinkle flour over the vegetable mixture and cook, stirring constantly, for about 1 minute. Gradually whisk in chicken broth and half-and-half. Bring to a boil, then reduce heat and simmer, stirring occasionally, until thickened, about 5-7 minutes.
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