In a large bowl, combine flour and sugar. Cut in butter until crumbly; stir in cheese and dill. In a small bowl, beat egg and milk; pour into dry ingredients and stir until moistened. (Batter will be very thick)
Pour into greased 8x4x2 inch loaf pan. Bake at 350 degrees F for 35-40 minutes or until bread is done. Cool in pan 10 minutes before removing.