Pat the chicken breasts dry with paper towels and season generously with salt and pepper on both sides. This helps develop a flavorful crust.
Heat the cast iron skillet over medium-high heat until it’s hot and shimmering, about 2-3 minutes. Add the olive oil, swirling to coat the bottom.
Place the chicken breasts into the skillet gently, laying them away from you to avoid splatters. Sear for about 5-6 minutes without moving, until the underside is golden brown and releases easily from the pan.
Flip the chicken and cook for another 5-6 minutes, until the opposite side is golden and the chicken is nearly cooked through. Use a meat thermometer to check for an internal temperature of 60°C / 140°F.
While the chicken cooks, whisk together honey, Dijon mustard, minced garlic, soy sauce, and apple cider vinegar in a small bowl until smooth. This creates your flavorful glaze.
Once the chicken reaches 60°C / 140°F, brush a generous layer of the honey mustard glaze over the top of each piece using a silicone brush. Continue cooking, flipping and glazing every 2 minutes, until the internal temperature hits 75°C / 165°F and the glaze is thick and caramelized, about 4 more minutes.
Flip the chicken one last time, apply a final layer of glaze, and cook for another minute to set the shine. The glaze should be glossy, sticky, and caramelized, with a smoky hue.
Remove the skillet from heat and let the chicken rest for 5 minutes on a cutting board. This helps the juices redistribute and keeps the meat juicy.
Slice the chicken against the grain, arrange on plates, and drizzle with any remaining glaze for extra shine and flavor. Serve immediately with your favorite sides.