Prep. Ensure the oven rack is set in the middle of the oven and preheat the oven to 425°F.
Make the biscuit dough by whisking together the all-purpose flour, baking powder, salt, and dried thyme in a large mixing bowl.
Scatter the cold butter pieces over the top of the dry ingredients. With a pastry blender (or your fingers), cut in the butter until the mixture resembles coarse crumbs (some pieces may be the size of small pebbles, and others as large as peas).
In a separate bowl or large measuring cup, whisk together the milk and Greek yogurt until combined. Stir in the cheese.
Pour the milk mixture into the dry ingredients a little at a time, lightly stirring with a rubber spatula between additions. Stop stirring as soon as the dough holds together (it will be very moist and seem wet, that's ok!).
Place in the fridge until ready to use.
Make the pot pie filling by heating the olive oil in 4-quart or larger Dutch oven (or ovenproof pot or skillet) over medium-high heat. Sauté the onion with the salt and pepper until the onion is tender and lightly browned (about 3 to 4 minutes). Add the garlic and cook until fragrant (about 1 minute more).
Sprinkle in the flour and stir it until it has soaked up any liquid and the onions look coated and a bit clumpy.
Stir in the chicken broth and milk. Bring the liquid to a low boil, then reduce the heat to simmer the ingredients, stirring constantly, until thickened (about 5 to 8 minutes).
Remove from the heat and stir in the chicken and the frozen peas and carrots.
Top the pot pie with the biscuits. Get the biscuit dough out of the fridge and divide the dough into 8 equal-sized pieces. Use your hands to shape each biscuit into ¼" - ½" thick discs / patties (it helps to grease or PAM your hands to do this!) and then place each biscuit on top of the pot pie filling, spacing them about ½-inch apart.
Bake the pot pie uncovered until the filling is bubbling and the biscuits are golden-brown (about 15 to 18 minutes). Let the pot pie cool for about 5 minutes before serving.
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Notes
Store leftover biscuit chicken pot pie in an airtight container in the fridge for 3-4 days. Reheat individual portions in the microwave until heated through. Alternatively, reheat in the oven at 350°F for 15-20 minutes, covering with tinfoil if the biscuits begin to brown too much.Variation Ideas:
Use leftover turkey from Thanksgiving! Replace the chicken one-for-one with your cooked and shredded (or cut up) turkey.
Use fresh thyme in your biscuits. Replace the 1 teaspoon of dried thyme leaves with 1 Tablespoon of fresh thyme leaves.
Bake the biscuits on a baking sheet instead of on top of the pot pie. This is a great option if you know you won't be serving up the entire pot pie at one time so the biscuits can be stored separately. My family doesn't mind how the biscuits when cooked and stored right on top of the pot pie, but if yours might, this is a good option for you.
Use a different type of biscuit, including store-bought. If using canned biscuits, brush them with melted butter before baking for best results.