In a small mixing bowl, mash the softened butter with the minced garlic, chopped rosemary, salt, and pepper. This creates a rich, fragrant mixture that will coat the chicken and help lock in flavor as it cooks.
Rub the herb butter generously all over the chicken thighs and drumsticks. Make sure to lift the skin and spread some underneath — that’s where the flavor really soaks in. Arrange the chicken pieces in your cast iron skillet in a single layer.
Preheat your oven to 425°F. Place the skillet inside and roast the chicken skin-side up for 15–20 minutes. The high heat will crisp up the skin while keeping the meat tender and juicy.
While the chicken is roasting, whisk together the balsamic vinegar and fig preserves in a small bowl. Stir until smooth — this will be your sweet and tangy glaze that ties the whole dish together.
After the initial roasting time, pull out the skillet and brush the chicken generously with the fig glaze. Return it to the oven for about 10 minutes, basting once or twice to build that gorgeous caramelized coating.
When the chicken is cooked through and the glaze is sticky and glossy, remove it from the oven. Give it a final drizzle of glaze and garnish with extra rosemary sprigs before serving.