Combine brown sugar and cornstarch in top of a double boiler; mix well. Add egg yolks, milk, and butter, mixing well. Cook over boiling water, stirring constantly, 30 minutes or until thickened. Remove from heat; stir in vanilla. Pour filling into pastry shell.
Beat egg whites (at room temperature) and cream of tartar until foamy. Gradually add 1/4 cup sugar, 1 tablespoon at a time, beating until stiff peaks form. Spread meringue over filling, sealing to edge of pastry. Bake at 350° for 10 minutes or until meringue is golden brown. Cool.