Season both sides of the chicken breasts with salt and pepper.
Lightly dredge the chicken in all-purpose flour, shaking off any excess.
Heat olive oil and 1 tablespoon of butter in a large skillet over medium-high heat.
Add the chicken breasts to the skillet and sear for 5 to 7 minutes per side until golden brown and the internal temperature reaches 165°F (74°C).
Remove the chicken from the pan and set aside on a plate.
Reduce the heat to medium and add the remaining 1 tablespoon of butter to the skillet.
Add the minced garlic and sauté for 30 to 60 seconds until fragrant but not browned.
Whisk in the honey, chicken broth, rice vinegar, thyme, and rosemary.
Simmer the sauce for 2 to 3 minutes until it thickens into a glaze-like consistency.
Return the chicken to the skillet and spoon the sauce over the breasts for 1 minute to coat thoroughly before serving.