01 - Set oven temperature to 400°F.
02 - Heat butter and olive oil in a large ovenproof pot over medium heat. Add diced onion, sliced carrots, and celery; cook until softened, approximately 5 to 6 minutes.
03 - Stir in minced garlic and cook for 1 minute. Sprinkle flour over vegetables and stir continuously for 2 minutes to eliminate raw flour taste.
04 - Gradually whisk in chicken broth, then add milk and heavy cream. Bring mixture to a simmer, stirring regularly until thickened, about 5 to 7 minutes.
05 - Stir in cooked chicken, frozen peas, frozen corn, dried thyme, dried parsley, salt, and black pepper. Simmer for an additional 5 minutes and then remove from heat.
06 - In a large bowl, combine flour, baking powder, baking soda, and salt. Cut in cold, cubed butter using a pastry blender or fork until mixture resembles coarse crumbs. Pour in cold milk and stir just until combined, avoiding overmixing.
07 - Drop spoonfuls of biscuit dough, approximately 2 tablespoons each, evenly atop the hot soup.
08 - Place the pot uncovered in the preheated oven and bake for 18 to 22 minutes, until biscuits achieve a golden-brown color and are fully cooked.
09 - Remove from oven and allow to cool briefly. Optionally garnish with chopped fresh parsley before serving warm.