In a medium bowl stir together the egg, oil, 1 tsp vanilla and 3/4 cup milk until well blended. Gradually stir in the sifted ingredients. Drop by tablespoonfuls onto the prepared cookie sheets. Bake for 10-12 minutes until firm. Allow to cool on cookie sheet for 5 minutes before moving to wire racks to cool completely.
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To make filling, in a medium saucepan whisk together the 1/2 cup milk and 2 1/2 tbsp flour. Cook over medium-high heat, stirring frequently until thick. Remove from heat and set aside to cool. In a medium bowl, beat together the shortening, 1/2 cup sugar, 1/2 tsp salt and 1 tbsp vanilla. Stir in the cooked mixture and beat for an additional 20 minutes, until really fluffy.
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