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Preheat oven to 425 degrees F.
In a 12-inch or larger oven-safe pan*, melt the butter over medium heat. Add the onion, carrots and celery and cook, stirring occasionally, until softened.
Stir in the garlic, thyme, salt, pepper and flour. Cook, stirring, for 1 minute.
Stir in the broth and milk and cook, stirring, until the mixture begins to bubble and thickens slightly, about 4-5 minutes. It will continue to thicken a little more as it bakes.
Turn off the heat and stir in the chicken and peas.
Whisk together the flour, baking powder and salt in a large bowl. Add the butter to the bowl and use a pastry cutter (or your fingertips) to work the butter into the flour until the largest butter pieces are the size of very small peas. Use a fork to stir in the milk until the dough clumps together.
Transfer the dough to a floured cutting board. Pat it down into a 3/4-inch thick round with your hands. Use a biscuit cutter or drinking glass to cut round biscuits.
Place the biscuits on top of the pot pie. Brush the biscuits with a little bit of milk. This will help the tops to brown in the oven.
Bake the pot pie for 15-18 minutes, until the biscuits are golden brown on top and the filling is bubbly.
Carefully remove the pan from the oven as it will be very hot. Serve.