Heat the oven to 400°F and bake the biscuits on a sheet pan for 7 minutes, then remove them while still pale.
Melt the butter in a large oven-safe skillet and cook the onion, carrots and celery until nearly tender, about 8 minutes.
Stir in the flour for 1 minute, then gradually add the broth and milk and simmer until thick.
Stir in the thyme, salt, black pepper, cooked chicken and peas and level the filling.
Set the partially baked biscuits over the hot filling with space between them.
Bake until the biscuits are deep golden and the filling bubbles, 18 to 22 minutes.