Slice both chicken breasts horizontally to form four even cutlets, then season both sides with salt and pepper. Even cutlets cook at the same pace and should lie flat without thick, raised centers.

Add the flour to a shallow dish and lightly coat each seasoned cutlet, shaking off the excess. The chicken should look lightly dusted rather than heavily breaded.

Set a large skillet over high heat and melt most of the butter, saving about 1 tsp for the garlic. The butter should be hot and foaming, but not browned or smoking.

Lay the chicken in the skillet and sear for 2 to 3 minutes before turning, then cook the second side for 1 minute. Flip when the first side has a deep golden crust and releases easily from the pan.

Reduce the heat slightly to medium-high once the chicken has browned. The skillet should remain lively but no longer look aggressively smoky.

Push the chicken aside, add the minced garlic with the reserved butter, and stir the garlic briefly as the butter melts. The garlic should smell fragrant within moments and remain pale, not dark brown.

Pour in the apple cider vinegar, soy sauce, and honey, then swirl or stir the skillet to combine. Bring the sauce to a simmer and cook for 1 minute, until rapid bubbles become glossy and slightly syrupy.

Turn the chicken through the glaze until every surface is coated, adding a touch of water if the sauce tightens too much. The finished glaze should flow slowly over the cutlets instead of forming a stiff candy-like layer.

Take the skillet off the heat, transfer the chicken to plates, and spoon the remaining glaze over the top. The chicken should look lacquered and the sauce should stay shiny as it settles.