Pat chicken thighs dry with paper towels and season generously with salt and pepper on both sides. This step ensures crispy skin and better browning—don't skip it even when time feels tight.
Heat olive oil in a large skillet over medium-high heat until shimmering, about 2 minutes. Place chicken thighs skin-side down and sear until golden brown, approximately 5-6 minutes without moving them.
Flip the chicken and sear the other side for 4-5 minutes until golden. Transfer to a plate temporarily while you build the sauce base with honey chicken thighs.
In the same skillet, combine minced garlic, Dijon mustard, honey, balsamic vinegar, apple cider, and chicken broth over medium heat. Stir constantly for 2-3 minutes until the mixture becomes fragrant and honey dissolves completely.
Return chicken thighs skin-side up to the skillet, nestling them into the sauce. Scatter baby potatoes, carrots, and sliced onion around the meat, then sprinkle thyme and rosemary over everything.
Reduce heat to medium-low, cover with a lid, and simmer for 18-20 minutes until potatoes are fork-tender and chicken reaches 165°F internal temperature. Uncover during the final 2 minutes to allow sauce to reduce.
In a small bowl, whisk cornstarch with 1 tablespoon cold water until smooth. Stir this slurry into the simmering sauce and cook uncovered for 1-2 minutes until thickened and glossy.
Remove from heat, swirl in butter for silky richness, and taste for seasoning adjustments before serving family chicken that looks restaurant-worthy.