Pat the chicken breasts dry and season both sides with salt and pepper. Lightly dredge each piece in flour, shaking off excess.
In a large skillet, heat olive oil and 1 tablespoon butter over medium-high heat. Add chicken and cook 4–5 minutes per side, until golden brown and cooked through. Remove to a plate.
Add remaining butter and minced garlic to the skillet. Sauté for 1 minute, stirring frequently.
Whisk in honey, soy sauce, apple cider vinegar, and red pepper flakes (if using). Bring to a simmer.
Return chicken to the skillet, spooning sauce over the pieces. Simmer 2–3 minutes until well coated. For a thicker sauce, stir in the cornstarch slurry and cook 1–2 more minutes.
Garnish with chopped green onions and sesame seeds. Serve hot with your favorite sides.