Combine flour and brown sugar in a medium mixing bowl; cut in butter using a pastry blender. Spoon half of mixture into pastry shell. Set remaining mixture aside. Arrange figs evenly over butter mixture.
Combine sugar and cinnamon; sprinkle evenly over figs. Combine egg, milk, and almond extract; beat well, and pour over figs. Top with remaining butter mixture.
Bake at 400° for 40 minutes. (Cover edges of pie with aluminum foil to prevent overbrowning, if necessary). Cool slightly.