Melt butter in a large pot over medium heat. Add the onion and carrot, and cook, stirring frequently until tender. Whisk in the flour and cornstarch, and cook for about a minute stirring constantly. Gradually whisk in the chicken stock and milk so that no lumps form.
Cook over medium heat, stirring constantly until the mixture is starting to thicken, 10 to 15 minutes. Remove from heat. Stir in the baking powder, and shredded cheese, and season with salt and pepper. Garnish with parsley before serving.
