Preheat your oven to 375°F. While it heats, prepare your mise en place: dice the onion and celery into 1/2-inch pieces, cut the carrots into 1/2-inch rounds, finely mince the garlic, and strip the thyme leaves from the sprigs (discard the woody stems). Have your shredded or bite-sized chicken pieces ready, measure out the flour, and set aside the frozen peas. Preparing everything upfront ensures smooth cooking without interruptions.

Melt 4 tablespoons butter in a large skillet over medium heat. Add the diced onion, carrots, celery, thyme leaves, salt, and black pepper. Sauté for 5-7 minutes, stirring occasionally, until the vegetables begin to soften and release their aromatics. Once softened, add the minced garlic and flour, stirring constantly for 30 seconds to 1 minute. This blooming process cooks out the raw flour taste and creates the base for a silky sauce.

Gradually pour in the chicken broth and milk while stirring constantly to prevent lumps from forming. Bring the mixture to a gentle boil over medium-high heat, then reduce the heat to medium and simmer for 4-5 minutes, stirring occasionally, until the sauce thickens enough to coat the back of a spoon. I like to simmer longer if the sauce seems too thin—a good filling should coat rather than pool at the bottom of the dish.

Remove the skillet from heat and stir in the cooked chicken and frozen peas from Step 1. Mix gently until everything is evenly distributed throughout the creamy sauce. Transfer the entire filling mixture into a 9x13-inch baking dish (or similar size casserole dish), spreading it in an even layer. The filling can be slightly warm or cooled slightly before topping—both work fine.

Arrange the refrigerated jumbo biscuits directly on top of the filling, spacing them evenly so they'll cook through without crowding. Melt 2 tablespoons butter and brush it generously over the top of each biscuit—this creates that beautiful golden-brown finish. I find it's easier to brush the biscuits after arranging them rather than before, so the butter stays on top where it belongs.

Place the baking dish in the preheated 375°F oven and bake for 20-30 minutes, until the biscuits are puffed and golden brown on top. The filling underneath should be gently bubbling around the edges. Remove from the oven and let rest for 2-3 minutes before serving—this allows the filling to set slightly and makes for cleaner portions.