Preheat the oven to 375 degrees F (190 degrees C).
Melt butter in an ovenproof skillet over medium heat. Sprinkle in flour and whisk continuously to make a roux, 1 to 2 minutes. Gradually add broth and milk whisking until thick, smooth, and bubbly, 4 to 5 minutes.
Stir in chicken, frozen vegetables, and onion. Cook for 1 to 2 minutes, then season with salt and pepper. Place biscuits on top of the chicken mixture, lightly pressing each down.
Bake in the preheated oven until biscuits are golden brown, 20 to 25 minutes. Check at about 15 minutes, and if biscuits are browning too quickly, cover with a piece of foil. Serve immediately.