Step 1: Prepare the Filling

1. Preheat the oven to 400°F (200°C).
2. In a large skillet or Dutch oven, melt the butter over medium heat. Add onion, carrots, and celery, and cook until softened (about 5 minutes).
3. Stir in garlic and cook for 30 seconds until fragrant.
4. Sprinkle flour over the vegetables and stir for 1 minute to form a roux.
5. Gradually whisk in chicken broth, followed by heavy cream, stirring constantly to avoid lumps.
6. Add salt, pepper, and thyme. Simmer until thickened, about 5 minutes.
7. Stir in shredded chicken and frozen peas. Remove from heat and pour into a greased 9×13-inch baking dish.

Step 2: Make the Biscuit Dough

1. In a large bowl, whisk together flour, baking powder, and salt.
2. Cut in cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.
3. Stir in buttermilk until just combined. Do not overmix.

Step 3: Assemble & Bake

1. Drop spoonfuls of biscuit dough evenly over the filling.
2. Brush the biscuit tops with melted butter for a golden finish.
3. Bake for 25–30 minutes, or until biscuits are golden brown and cooked through.
4. Let cool for 5 minutes before serving.