Preheat the oven to 190 degrees C (375 degrees F). Grease cookie trays.
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 1.5cm in diameter. Cut snakes into 5cm pieces. Dip each piece in remaining milk, then roll in sesame seeds. Place 2.5cm apart onto the prepared cookie trays.
Bake for 20 to 25 minutes in the preheated oven, or until golden brown. Remove from cookie trays to cool on wire racks.