01 - Preheat your oven to 425°F (220°C). Line a baking sheet with parchment paper, which will be used for the biscuits.
02 - In a large pot or Dutch oven, melt the butter and olive oil over medium heat. Add the diced onion, carrots, and celery. Sauté until the vegetables have softened, approximately 5 minutes.
03 - Add the minced garlic to the pot and cook for about 30 seconds until fragrant. Sprinkle the all-purpose flour over the vegetables and cook, stirring constantly, for 2 minutes to create a roux.
04 - Gradually whisk in the chicken broth, ensuring that no lumps remain. Add the diced potatoes, dried thyme, dried parsley, salt, and black pepper. Bring the mixture to a simmer and cook for 10 minutes, or until the potatoes are tender.
05 - Stir in the cooked chicken breast, frozen peas, and frozen corn. Allow the soup to simmer for an additional 5 minutes.
06 - Reduce the heat to low and stir in the heavy cream. Taste and adjust the seasoning as needed. Keep the soup warm over low heat.
07 - While the soup is simmering, prepare the biscuits. In a large bowl, whisk together the all-purpose flour, baking powder, baking soda, and salt. Add the cold, cubed butter and cut it into the dry ingredients using a pastry cutter or your fingertips until the mixture resembles coarse crumbs.
08 - Pour in the cold buttermilk and mix just until the dough begins to come together. Turn the dough onto a lightly floured surface and gently pat it to a thickness of 1 inch. Use a 2.5-inch round cutter to cut out the biscuits.
09 - Place the cut biscuits onto the prepared baking sheet. Brush the tops of the biscuits with a little additional buttermilk. Bake for 12–15 minutes, or until the biscuits are golden brown.
10 - Serve the hot soup in bowls with the freshly baked biscuits on the side for dipping.