Step 1

Arrange a rack in the middle of the oven and heat to 425°F.

Step 2

Whisk the flour, cheese, thyme, baking powder, and salt together in a medium bowl. Add the cream and use a wooden spoon to stir until a shaggy dough forms. Refrigerate while you prepare the pot pie.

Step 3

Heat olive oil in a 3-quart (or large) Dutch oven or ovenproof pot over medium-high heat until shimmering. Add the onion and sauté until tender and lightly browned, 3 to 4 minutes. Add the garlic and cook 1 minute more. Sprinkle in the flour and stir until the flour dissolves. Stir in the chicken broth and milk. Bring to a boil, then reduce the heat and simmer, stirring constantly, until thickened, 5 to 8 minutes.

Step 4

Remove from the heat and stir in the chicken, peas and carrots, salt, and pepper. Divide the biscuit dough into 6 portions (about 2 heaping tablespoons each). Use your hands to shape each biscuit into a 1/2-inch-thick patty and place on top of the chicken mixture, spacing them about 1/2-inch apart.

Step 5

Bake uncovered until heated through and bubbling and the biscuits are golden-brown, 15 to 18 minutes. Let cool about 5 minutes before serving.