Preheat oven to 200°C Lightly grease a 12-hole, 1/3 cup-capacity muffin pan.
Sift flour into a large bowl. Make a well in centre. Pour butter, egg and milk into a jug. Stir to combine. Pour into well. Stir until almost combined. Fold through feta, ham, tomatoes and olives.
Spoon mixture into muffin holes. Insert a rosemary sprig in the top of each muffin. Bake for 20 minutes or until a skewer inserted in the centre comes out clean. Set aside in pan for 1 minute. Turn out onto a wire rack to cool completely. Place muffins in an airtight container. Serve with butter.