Preheat the oven to 400°F (200°C).

In a large skillet or saucepan, melt butter over medium heat. Add diced onion, carrots, and celery, and cook until softened, about 5 minutes. Stir in the garlic and cook for another minute.

Sprinkle flour over the vegetables and cook for 1-2 minutes, stirring constantly. Gradually add chicken broth, stirring to prevent lumps. Let simmer until thickened.

Add heavy cream, cooked chicken, peas, thyme, salt, and pepper. Stir and let the mixture simmer for a few minutes.

For the biscuit topping, whisk together flour, baking powder, and salt. Cut in cold butter using a pastry cutter or fork until the mixture resembles coarse crumbs.

Gradually add cold buttermilk, stirring until just combined. Drop spoonfuls of the biscuit dough on top of the chicken filling.

Transfer the skillet to the oven and bake for 20-25 minutes or until the biscuits are golden brown and cooked through.

Let the dish cool for a few minutes before serving. Garnish with fresh parsley if desired.