Heat the oven to 425°F and melt the butter in a 12-inch ovenproof skillet over medium heat.
Cook the onion for 4 minutes, stir in the flour for 1 minute and gradually whisk in the broth and milk.
Simmer until thick enough to coat a spoon, then fold in the fully cooked chicken, vegetables and thyme.
Arrange the split biscuits in one layer over the filling and transfer the skillet to the oven.
Bake for 16 to 20 minutes, until the biscuits are browned, their centers are baked through and the filling reaches 165°F.