01 - Preheat the oven 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 5 to 6 minutes until softened.
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 followed by whole milk and heavy cream. Bring mixture to a simmer, stirring frequently until thickened, about 5 to 7 minutes.
05 - Stir in cooked chicken, frozen peas, corn, dried thyme, dried parsley, salt, and pepper. Simmer for 5 minutes to heat thoroughly, then remove from heat.
06 - In a large bowl, combine all-purpose flour, baking powder, baking soda, and salt. Cut in cold butter using a pastry blender or fork until mixture resembles coarse crumbs.
07 - Add cold whole milk to the dry mixture and stir until just combined; avoid overmixing.
08 - Drop spoonfuls (about 2 tablespoons each) of biscuit dough evenly over the hot soup surface.
09 - Place the pot in the preheated oven and bake uncovered for 18 to 22 minutes until biscuits are golden and cooked through.
10 - Remove from oven, allow to cool for a few minutes, then sprinkle with fresh parsley if desired. Serve warm.