Prepare the biscuits, following the homemade biscuit recipe here. To prepare the chicken, combine 4 tablespoons of the butter with the flour in a small bowl. Set aside.
Dissolve the cornstarch in the milk in a separate bowl and set aside.
Add two tablespoons of butter to a large saucepan, add the onion, carrot, and celery and saute over medium-high heat for about 5 minutes.
Pour in 1 cup of broth, reserving 1/4 cup for later, and bring to a boil. Cover and simmer for about 10 minutes or until the vegetables are just tender.
Add the potatoes, bring to a boil, cover and continue simmering for about 12 minutes, or until the potatoes are fully cooked.
Add the butter and flour mix and bring to a gentle boil, constantly stirring.
Pour in the milk and cornstarch mixture and bring to a boil. Add salt and pepper to taste. Stir in the chicken and peas. Add a more broth, one tablespoon at a time, if the mixture is too thick for your taste.
Ladle the chicken mixture into 4 small bowls or ramekins, a cup or slightly larger. Place a warm biscuit on top and serve.