Preheat your oven to 375°F. Lightly grease a 9×13-inch baking dish or a deep 10-inch oven-safe skillet with non-stick cooking spray and set it aside.
Melt the 4 tablespoons of unsalted butter in a large skillet or Dutch oven set over medium heat. Drop in the chopped onion and sauté for 4 to 5 minutes until soft and translucent. Add the minced garlic and cook for 1 additional minute until highly fragrant.
Sprinkle the ⅓ cup of all-purpose flour evenly over the sautéed aromatics. Stir continuously for 1 to 2 minutes to toast the flour starches and eliminate the raw flour taste. The mixture will form a thick paste.
Slowly pour in the chicken broth a little at a time, whisking vigorously to dissolve the flour paste completely and prevent lumps from forming. Once smooth, stir in the heavy cream.
Bring the liquid to a gentle simmer over medium heat. Let it cook for 3 to 4 minutes, stirring often, until the sauce thickens into a rich, glossy gravy baseline that coats the back of a spoon.
Stir in the dried thyme, garlic powder, salt, black pepper, diced cooked chicken, and the frozen peas and carrots. Let the entire filling matrix simmer together for 2 minutes until heated through. Taste and adjust seasonings if preferred.
Pour the hot chicken filling directly into your prepared 9×13-inch baking dish (or leave it right in your skillet if using an oven-safe pan). Smooth it into a flat, level layer.
Pop open the can of refrigerated biscuits. Arrange the individual dough rounds flat across the top of the hot chicken mixture, leaving a fraction of an inch of space between them to allow for steam expansion during baking. Pro Tip: For a bite-sized top crust, use a kitchen knife to quarter each biscuit piece and scatter the dough dough pieces evenly over the top.
Place the dish on the middle oven rack and bake at 375°F for 20 to 22 minutes. Watch the topping closely; it is finished the exact moment the biscuit crowns puff up fully and take on a beautiful, rich golden-brown color.
Remove the pot pie bake from the oven and let it sit undisturbed on a cooling rack for 5 minutes. This cooling window allows the savory gravy baseline to settle slightly so it isn't too runny when scooped. Serve hot.