Preheat the oven to 425°F (220°C).
In a large bowl, whisk together the balsamic vinegar, honey, whole grain mustard, minced garlic, salt (about 1/2 teaspoon) and pepper (about 1/4 teaspoon) until combined.
Add the chicken thighs to the bowl and toss to coat; marinate at room temperature for 20 minutes or refrigerate for up to 1 hour.
Remove the chicken from the marinade and reserve the marinade; pat the chicken dry with paper towels.
Heat the olive oil in a 12-inch oven-safe skillet over medium-high heat until shimmering.
Place the chicken in a single layer, skin-side down, and cook until the skin is browned and crisp, about 2 to 3 minutes.
Flip the chicken, add the tomatoes to the skillet, and cook until the tomatoes begin to pop and release juices, about 5 minutes.
Pour the reserved marinade over the chicken, add the broken rosemary sprigs, bring to a boil on the stove, then transfer the uncovered skillet to the preheated oven.
Bake until the chicken reaches an internal temperature of 165°F (74°C), about 20 minutes more; remove from oven and discard rosemary stems before serving.