Melt butter in a Dutch oven or oven-safe pot over medium heat, then sauté chopped onion, carrots, and celery for 5-7 minutes until softened, and stir in dried thyme.
Sprinkle flour over the vegetables and stir continuously for 1-2 minutes to cook out the raw flour taste, creating a roux.
Gradually whisk in chicken broth, then milk, stirring constantly until the mixture thickens into a gentle simmer.
Stir in frozen peas, frozen corn, and cooked chicken, then season with salt and pepper to taste; remove from heat and set aside.
Preheat oven to 400°F (200°C). In a large bowl, whisk together the dry biscuit ingredients: flour, baking powder, baking soda, sugar, garlic powder, and salt.
Add cold, cubed butter to the dry ingredients and cut it in with a pastry blender or fingertips until the mixture resembles coarse crumbs with pea-sized butter pieces.
Pour in the buttermilk and stir gently with a fork until just combined, being careful not to overmix, then fold in the shredded cheddar cheese.
Spoon the chicken pot pie filling into a 9x13 inch baking dish (or use the oven-safe pot). Drop spoonfuls of biscuit dough evenly over the hot filling, forming rough shapes or dollops.
Bake for 25-30 minutes until the biscuits are golden brown and cooked through, and the filling is bubbling around the edges.
While the pot pie bakes, melt butter in a small microwave-safe bowl, then stir in minced garlic and optional chopped parsley.
Once the pot pie is out of the oven, brush the warm garlic butter mixture over the hot biscuits; let it rest for 5-10 minutes before serving to allow the filling to set slightly.
