Melt butter and brown sugar in skillet; brown carefully so it doesn't burn. Gradually add water.
Beat egg yolks and add small amount of milk, all of the flour and salt. Mix until smooth; add remaining milk. Pour slowly into sugar mixture. Cook over low heat until thick. Pour into cooked shell.
For meringue, beat egg whites and 1/2 cup white sugar until fluffy. Spread meringue over pie filling. Brown in oven at 350 degrees for about 10 to 15 minutes. Watch carefully.