Preheat the oven to 375 degrees F (190 degrees C). Grease cookie sheets.
In a large bowl, stir together the flour, sugar, baking powder and salt. Blend in butter and shortening until the mixture resembles coarse meal. Make a well in the center and add eggs, 1/4 cup of milk and vanilla.
Mix until a soft dough forms. Divide the dough into 4 pieces.
Roll each piece out into a long snake 1/2 inch in diameter.
Cut snakes into 2 inch pieces. Dip each piece in remaining milk, then roll in sesame seeds.
Place 1 inch apart onto the prepared cookie sheets.
Bake for 20 to 25 minutes in the preheated oven, or until golden brown.
