Heat the oven to 400°F and grease a 9-by-13-inch baking dish.
Melt the butter in a large skillet over medium heat and cook the onion, carrots and celery for 8 minutes, until the onion is translucent.
Stir in the flour and cook for 1 minute, then gradually whisk in the broth and milk until smooth.
Simmer for 4 to 6 minutes, stirring, until the gravy coats the back of a spoon, then add the chicken, peas, thyme, salt and pepper.
Spread the hot filling in the baking dish and arrange the separated biscuits on top with a little space between them.
Bake for 22 to 27 minutes, until the biscuits are deeply golden, cooked through underneath and the filling reaches 165°F.
Rest for 8 minutes before serving because the filling is hotter than it looks.