Pulse together the flour, baking powder, sugar and 1 tablespoon salt in a food processor. Add the butter and pulse until pea-sized pieces. Add the buttermilk and pulse a couple of times until the dough just comes together but is not fully incorporated. Transfer to a bowl, cover and refrigerate while you make the skillet sauce.
Whisk the chicken broth and mashed potatoes together in a large cast iron skillet and bring to a simmer over medium-high heat. Stir in the fried chicken and peas and carrots and top evenly with heaping tablespoons of dough.
Transfer to the oven and bake until golden brown and bubbly, 40 to 45 minutes. Let rest for 10 minutes before serving.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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