Heat the oven to 400°F and butter a 9-by-13-inch baking dish with 1 teaspoon of the butter.
Melt the remaining butter in a large skillet over medium heat and cook the onion for 6 minutes, until soft.
Stir in the flour and cook for 1 minute, then whisk in the broth and milk gradually.
Add the salt and pepper and simmer for 4 to 6 minutes, until the gravy is thick enough to leave a trail across the skillet.
Fold in the chicken and peas and carrots, heat for 2 minutes, and spread the filling in the dish.
Arrange the biscuits over the hot filling with about 1 inch between them.
Bake for 25 to 30 minutes, until the biscuits are browned and cooked through and the filling reaches 165°F.
Rest for 5 minutes before spooning out one biscuit with each serving.