Preheat oven to 400 degrees F. Spray a 9x13 baking dish with nonstick spray.
Add 4 tablespoons of butter into a large pot to melt. Add onions and celery and sauté for 5 minutes, until vegetables have softened. Add the frozen vegetables and sauté for an additional 5 minutes.
Sprinkle ½ cup flour, salt, and pepper over sautéed vegetables and stir to coat evenly. Stir constantly for 2 minutes, letting the flour cook a bit. This mixture will be thick and pasty.
Pour in chicken stock and stir mixture constantly as it comes to a low boil.
Reduce heat to medium low and add the milk, stirring constantly.
Add the chicken to the pot and stir to combine. Simmer for 15 minutes, stirring occasionally, while making the biscuits. Taste and season with additional salt and pepper, if needed.
Carefully pour the filling into the prepared baking dish. Top with the biscuits. Lightly brush the biscuit tops with 2 tablespoons of melted butter.
Bake for 20 minutes, until the filling is bubbly, and the biscuits are golden brown. Gently lift the top of a biscuit to make sure that the biscuit is cooked through and not too gooey on the bottom. It will be a bit wet, of course, but should not be gooey.
Let sit for 5 minutes before serving.