Pat the chicken breasts dry with paper towels to remove excess moisture, which helps achieve a good sear.
Whisk together honey, Dijon mustard, apple cider vinegar, smoked paprika, lemon juice, and olive oil in a small bowl until well combined and slightly thickened.
Preheat your grill or grill pan over medium-high heat until it reaches about 200°C / 390°F. Lightly oil the grates to prevent sticking.
Place the chicken breasts on the hot grill, hearing a satisfying sizzle as they make contact. Cook for 6-7 minutes without moving them, until the underside develops a golden-brown crust and slight charring.
Use tongs to flip the chicken breasts gently, then cook for another 6-7 minutes, maintaining a steady sizzle and checking for even browning.
Baste the chicken with the honey-mustard glaze during the last 2 minutes of cooking, brushing it on evenly to create a sticky, caramelized coating.
Insert a probe thermometer into the thickest part of a chicken breast; once it reads 74°C / 165°F, remove the chicken from the grill and transfer to a plate.
Let the chicken rest for 5 minutes under foil to allow the juices to redistribute and keep the meat moist.
Slice the chicken or serve whole with a sprinkle of fresh herbs if desired. The exterior should be beautifully caramelized with a smoky aroma, and the interior tender and juicy.