Combine flour, baking powder and sugar in a bowl. Cut in shortening with a pastry blender-or work with your hands - until mixture resembles coarse meal. In separate bowl, mix eggs, milk and vanilla and add to flour mixture mixing until dough holds together (if needed, add more milk).
Pull off small portions of dough and roll between palms of the hands making a log. Cut into 2" pieces and roll in sesame seeds. Place on ungreased baking sheet.
Bake at 350° for 20 to 25 minutes, or until golden brown. Remove, cool completely, then store in an Airtight container