Preheat the oven to 400°F (200°C).
In a large oven-safe pot or Dutch oven, melt 2 tablespoons of butter over medium heat.
Add the diced onion, carrots, and celery to the pot and cook until softened, about 5-7 minutes.
Stir in the minced garlic and cook for 1 minute until fragrant.
Sprinkle 1/3 cup of flour over the vegetables and stir well to coat. Cook for 2 minutes to remove the raw flour taste.
Gradually whisk in 2 cups of chicken broth and 1 cup of milk, stirring constantly until the mixture thickens and becomes creamy, about 4-5 minutes.
Add 1 teaspoon dried thyme, 1/2 teaspoon salt, and 1/4 teaspoon black pepper. Stir to combine.
Add the cooked chicken, frozen peas, and frozen corn. Stir well and remove the pot from heat.
In a medium bowl, combine 1 1/2 cups flour, 2 teaspoons baking powder, and 1/2 teaspoon salt.
Cut in 6 tablespoons of cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs.
Pour in 3/4 cup whole milk and stir just until the dough comes together.
Drop spoonfuls of the biscuit dough evenly over the chicken mixture in the pot.
Place the pot uncovered in the preheated oven and bake for 20-25 minutes, or until the biscuit topping is golden brown and cooked through.
Remove from the oven and let cool for 5 minutes before serving.