Slice each chicken breast horizontally to make 4 thin steaks. Season both sides with salt and pepper.
Place flour in a shallow dish. Lightly coat chicken, shaking off excess.
Heat most of the butter in a large skillet over high heat, reserving about 1 teaspoon.
Cook chicken for 2–3 minutes until golden. Flip and cook the other side for 1 minute.
Reduce heat to medium-high. Push chicken aside, add garlic and remaining butter, and stir briefly.
Add vinegar, soy sauce, and honey. Stir to combine and bring to a simmer. Simmer 1 minute until slightly thickened.
Turn chicken to coat in sauce. Add a splash of water if sauce becomes too thick.
Remove from heat immediately. Serve hot with extra honey garlic sauce spooned over the top.