Preheat oven to 425°F.

Melt butter in a large saucepan over moderate heat, blend in flour, add milk and broth, and heat, stirring, until thickened. Add chicken and all seasonings, cover, and simmer 5-10 minutes, stirring occasionally. Cool to room temperature.

Mix in carrots and peas and spoon into an ungreased 2½-quart casserole about 9” in diameter.

Prepare pastry and roll into a circle 3” larger than casserole; make 3 V-shaped steam slits near center. Dampen casserole rim, fit pastry on top, roll pastry edges under even with rim, and crimp to seal. Brush with glaze, being careful not to cover slits.

Bake 30-40 minutes until browned and bubbly (place a sheet of foil on rack under casserole to catch drips). To serve, cut wedges of pastry and ladle chicken mixture on top.

FOR THE PASTRY

Place flour and salt in a shallow mixing bowl and cut in shortening with a pastry blender until mixture resembles coarse meal. Sprinkle water over surface, 1 tablespoon at a time, and mix in lightly and quickly with a fork, just until pastry holds together.

Shape gently into a ball on a lightly floured pastry cloth, then flatten into a circle about 1” thick, evening up rough edges.