Heat oven to 400°F. In large saucepot, melt butter over medium-high heat. Stir in flour, pepper, thyme, and nutmeg. Cook, stirring, for 3 minutes. Whisk in chicken broth and half-and-half. Bring to a boil, and cook over medium-high heat, whisking constantly for 3 minutes. Stir in mixed vegetables and chicken. Divide mixture among 8 one-cup baking dishes, or spoon into 2-quart baking dish.
Unfold pie crust; use fluted pastry wheel or pizza cutter to cut pastry into randomly shaped pieces. Place pieces over top of filling, overlapping edges to create a patchwork pattern. Bake 30 minutes, or until pastry is golden brown.