Preheat the oven to 190 degrees C. Grease baking trays.
In a large bowl, stir together the flour, sugar, baking powder and salt. Blend in butter until the mixture resembles coarse meal. Make a well in the centre 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 1cm in diameter. Cut snakes into 5cm pieces. Dip each piece in remaining milk, then roll in sesame seeds. Place 3cm apart onto the prepared baking trays.
Bake for 20 to 25 minutes in the preheated oven, or until golden brown. Remove from baking trays to cool on wire racks.