Preheat the oven to 425 degrees F (220 degrees C). Butter a 9-inch deep-dish pie pan with 1 tablespoon melted butter.

Combine mixed vegetables and chicken in a saucepan over medium heat; cook until vegetables are tender, 5 to 7 minutes. Fold in condensed soup; mix well. Pour in milk and mix until smooth; mixture should not be runny. Season with salt and pepper; bring to a boil.

Remove from the heat and spread mixture into the bottom of the prepared pie pan. Separate biscuits into layers and place gently on top of chicken-vegetable mixture. Drizzle remaining 2 tablespoons melted butter over biscuits.

Bake in the preheated oven until golden brown, about 15 minutes.

Remove from the oven and let stand for 15 minutes before serving.