Preheat the oven to 425 degrees F.

In a deep 12-inch cast iron skillet or oven safe Dutch oven, melt the butter over medium high heat. Add the onion, carrots, and celery; cook until tender, stirring occasionally, about 5 minutes. Add the garlic and cook for 1 minute.

Stir in flour until lightly browned, about 1 minute. Add the thyme, salt, and pepper.

Slowly pour in the chicken broth and heavy cream. Bring to a boil; reduce heat and simmer, stirring occasionally, until slightly thickened, about 3 to 5 minutes.

Stir in the chicken, peas, and parsley. Season with additional salt and pepper, if necessary. Turn off the heat and set aside while you make the biscuits.

To make the biscuits, whisk together the flour, baking powder, baking soda, sugar, and salt in a large bowl. Set aside.

In a medium bowl, combine cold buttermilk and the 1/2 cup slightly cooled melted butter. Stir with a spatula until combined and small clumps form. It is ok if the mixture is lumpy.

Add buttermilk mixture to dry ingredients and stir with rubber spatula until just combined and the biscuit batter pulls away from sides of bowl.

Use a large cookie scoop or a greased 1/4 cup measuring cup to scoop out the dough. Drop the biscuit dough on top of the filling, leaving a little space between each biscuit because they will spread a little in the oven. Brush with the extra melted butter.

Carefully transfer the skillet to the hot oven and bake for 14 to 17 minutes or until the biscuits are lightly golden brown on top.

Remove from oven and let stand for 10 minutes before serving.