Preheat the Oven: Set to 400°F (200°C).
Prepare the Filling: In a large oven-safe skillet, melt butter over medium heat. Sauté onions, garlic, and carrots until softened (about 5 minutes).
Thicken the Sauce: Stir in flour and cook for 1 minute. Gradually add chicken broth while stirring. Pour in heavy cream, add peas, corn, shredded chicken, thyme, salt, and pepper. Let simmer for 3-5 minutes until thickened. Remove from heat.
Make the Biscuits: In a bowl, whisk flour, baking powder, garlic powder, salt, and sugar. Cut in cold butter until crumbly. Stir in cheese and milk until just combined.
Assemble & Bake: Drop spoonfuls of biscuit dough on top of the filling. Bake for 25-30 minutes, or until biscuits are golden brown.
Brush & Serve: Mix melted butter with garlic powder and parsley, then brush over the biscuits. Serve hot!