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Preheat oven to 425 degrees F. In a large bowl, combine balsamic vinegar, honey, mustard, and garlic and desired amount of salt and pepper.
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Whisk until combined.
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Pour mixture in a Ziploc bag and add chicken thighs. Seal and toss until fully coated.
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Let the chicken thighs marinate in the fridge for at least 20 minutes.
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Heat olive oil in a large cast iron skillet over medium-high heat.
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Add chicken, skin side down for 2 minutes, then flip and sear 2 minutes more. Add remaining marinade and and rosemary sprigs.
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Transfer cast iron skillet to the oven and bake for 25 minutes, or until chicken is fully cooked.