It's hard to imagine a more comforting combination than a savory chicken pot pie filling topped with cheesy biscuits. Butternut squash replaces the usual potatoes for a nice hit of color and sweetness.
Note: Using precooked rotisserie chicken meat saves valuable prep time.
Make-ahead tip: Prepare pies up to the point of baking; then wrap tightly in foil and freeze for up to 3 months. When ready to use, thaw in refrigerator and bake as directed.
First, make the filling: In a medium-size saucepan over high heat, bring chicken broth to a boil. Add carrots and squash. Reduce heat to medium-low and simmer until vegetables are tender, 5 to 7 minutes. Drain vegetables, reserving broth. Set aside.
Melt butter in a large skillet over medium heat. Add celery, onion, and salt; cook until golden, 10 to 12 minutes. Add mushrooms and cook until they release most of their liquid, 5 to 7 minutes. Add flour and cook, stirring, about 2 minutes. Add milk slowly, whisking as you go; then add reserved broth, whisking until smooth. Cook, stirring often, until sauce thickens, 8 to 10 minutes. Season with pepper. Add parsley, chicken, reserved vegetables, and peas. Divide filling evenly among 6 ramekins or other 8- to 10-ounce ovenproof bowls, leaving about a half-inch at the top for biscuits. If you have extra filling, put it in another ramekin.
Preheat oven to 425°. Make the biscuits: In a large bowl, whisk flour with baking powder, baking soda, and salt. Use your fingers to smear the butter into the flour mixture until it resembles coarse meal, with plenty of lumps. Stir in cheddar and scallions. In a medium-size bowl, whisk together egg and buttermilk; then add to flour mixture. Stir with a fork until a shaggy dough forms.
Divide dough into 2 balls. On a lightly floured counter, press dough out to a half-inch thickness. Using a biscuit cutter or the floured rim of a glass, cut out 2- to 3-inch rounds. Gather dough again as needed and press out again. Repeat with second ball.
Divide biscuits among ramekins, overlapping as necessary. Brush tops with milk, and set ramekins on a baking sheet lined with foil. Bake until crust is nicely browned and filling is bubbling, about 20 minutes.