Preheat oven to 375°F. In large bowl, whisk flour, dill, baking powder, baking soda and salt. Stir in 1 cup of the cheese, tossing to coat cheese. In separate bowl beat butter and sugar with electric mixer until smooth. Beat in eggs. Stir in apple and milk. Stir wet ingredients into flour mixture just until combined.
Pour batter into greased 9x5-inch loaf pan; sprinkle with remaining 1/4 cup cheese.
Bake 45 to 50 minutes, or until toothpick inserted in center comes out clean. Cool in pan on wire rack 10 minutes. Remove from pan and cool completely.