Preheat the oven to 400°F (200°C) and gather all ingredients.

Melt 3 tablespoons butter in a large oven-safe skillet over medium heat. Add diced onion; cook 3 minutes until softened. Stir in minced garlic and cook 30 seconds.

Sprinkle 2 tablespoons flour over the onions and garlic, stirring constantly for 1 minute to form a roux.

Slowly whisk in 2 cups chicken broth. Continue whisking until the mixture is smooth and starts to thicken, about 2–3 minutes.

Add 1 cup heavy cream, dried thyme, dried rosemary, salt, and pepper. Stir to combine and taste for seasoning.

Fold in cooked chicken and frozen peas and carrots; simmer 2 minutes until vegetables are heated through. Remove skillet from heat.

In a mixing bowl, whisk 2 cups flour, baking powder, and 1 teaspoon salt. Cut in 6 tablespoons cold butter until mixture resembles coarse crumbs.

Pour in 3/4 cup buttermilk and stir just until dough comes together. Drop heaping spoonfuls of dough evenly over the hot chicken filling, leaving small gaps between biscuits.

Brush biscuit tops with 2 tablespoons melted butter. Transfer skillet to the oven and bake 18–22 minutes, or until biscuits are golden brown and cooked through.

Remove from oven and let rest 5 minutes before serving hot.