Preheat oven to 375°F; grease a 9x13-inch dish and set aside.
Melt butter in a large skillet over medium; cook onion about 5 minutes until softened, then garlic 1 minute more.
Sprinkle flour over onions; stir to coat and cook 2 minutes, stirring constantly.
Gradually whisk in broth and cream; simmer about 5 minutes, stirring frequently, until thickened.
Add chicken, vegetables, thyme, salt, and pepper; cook 2-3 minutes until vegetables are warmed through.
Spread chicken mixture evenly in dish.
Separate biscuits; quarter each and arrange evenly over filling.
Bake 25-30 minutes until biscuits are golden brown and filling bubbles at edges; cool 5 minutes before serving.