01 - Preheat oven to 400°F.
02 - Heat butter and olive oil in a large ovenproof pot over medium heat. Add onion, carrots, and celery; cook until softened, about 5–6 minutes.
03 - Stir in garlic and cook for 1 minute. Sprinkle flour over vegetables and stir continuously for 2 minutes to eliminate raw taste.
04 - Gradually whisk in chicken broth, then add whole milk and heavy cream. Bring mixture to a simmer, stirring until thickened, 5–7 minutes.
05 - Add cooked chicken, peas, corn, thyme, dried parsley, salt, and pepper. Simmer for 5 minutes to heat through. Remove from heat.
06 - In a large bowl, whisk flour, baking powder, baking soda, and salt. Cut in cold butter using a pastry blender or fork until mixture forms coarse crumbs.
07 - Pour in cold milk and stir gently until just combined; avoid overmixing.
08 - Drop biscuit dough by spoonfuls (approximately 2 tablespoons each) evenly over the hot soup in the pot.
09 - Place pot uncovered in the preheated oven and bake for 18–22 minutes until biscuits are golden brown and cooked through.
10 - Remove from oven, allow to cool slightly, garnish with fresh parsley if desired, and serve warm.