Preheat oven to 400 degrees F.
Prepare the Bottom Crust: In a medium bowl, use a pastry blender to cut the butter into the Bisquick until the mixture resembles coarse crumbs. Using a wooden spoon, stir in the milk until the mixture begins to form a ball. Pat the dough onto the bottom and up the sides of a 9-inch pie plate. Bake for 5 minutes, or until just turning light brown. Remove from the oven and set aside.
Prepare the Filling: Heat the butter in a 2-quart saucepan over medium heat until melted. Using a wooden spoon, stir in the Bisquick, chopped onion, salt and pepper. Cook, stirring constantly, until the mixture is bubbly. Remove from the heat. Gradually stir in the chicken broth, then stir in the frozen vegetables.
Return the mixture to the stove over medium heat, stirring constantly, until the mixture reaches a boil. Once a full boil is reached, continue stirring for another 1 minute. Remove from the heat and stir in the chicken. Pour the chicken mixture into the prepared crust.
Prepare the Top Crust: In a small bowl, whisk together the Bisquick, milk and melted butter until smooth. Pour the mixture evenly over the filling. Use a rubber spatula or offset spatula to gently spread it to the edge of the pie plate.
Bake for 25 minutes, or until the top is golden brown. Let stand for 10 minutes before serving.