Preheat oven to 375°F.
Heat a 12-inch cast iron skillet over medium heat. Melt the butter and add the diced onion. Cook 4–5 minutes until softened. Add garlic and cook 30 seconds.
Sprinkle the flour over the onion mixture and stir well. Cook for 1 minute.
Slowly whisk in the milk, then the chicken broth. Stir constantly until smooth. Add salt, pepper, and thyme.
Simmer for 3–5 minutes until the sauce thickens and coats the back of a spoon.
Stir in the cooked chicken and frozen vegetables. Remove from heat.
Evenly place biscuit pieces on top of the filling. Do not press them down.
Transfer skillet to the oven and bake for 30–35 minutes, or until biscuits are golden brown and cooked through.
Let rest 5–10 minutes before serving.