Preheat the oven. Set the oven to 375°F and have a 9×13-inch baking dish ready.
Cook the onions. Heat the cooking oil in a large pot over medium heat. Add the diced onion and sauté until softened and beginning to brown.
Make the creamy sauce. Add the butter and let it melt. Stir in the flour and cook for approximately 1 minute. Slowly whisk in the milk, followed by the chicken broth, until incorporated. Continue cooking and stirring until the sauce begins to thicken.
Add the chicken and vegetables. Stir in the poultry seasoning, thawed mixed vegetables, and chopped cooked chicken. Mix until everything is coated in the creamy sauce, then remove from the heat.
Prepare the biscuit topping. Combine the Cheddar Bay biscuit mix with the garlic powder and onion powder. Add the water and shredded cheese according to the package directions, mixing until a biscuit dough forms.
Assemble the pot pie. Transfer the creamy chicken mixture to the baking dish. Drop spoonfuls of biscuit dough evenly across the filling, leaving the biscuits in separate portions rather than spreading the dough into one solid layer.
Bake. Bake for approximately 20 minutes, or until the biscuits are cooked through and the filling is hot. If the biscuits need additional browning, briefly broil the tops while watching closely.
Add the finishing butter. Prepare the melted butter with the seasoning packet included in the biscuit mix according to its directions. Brush over the warm biscuits before serving.