Drain cherries, pouring liquid into a small saucepan. Add apple juice, honey, and butter. Heat on low heat until butter is melted. Stir well.
In a 9-inch square baking pan, mix cherries and diced apples. Mix together flour and cinnamon. Sprinkled over fruit and toss gently. Add 1 cup of the heated fruit juice mixture.
Dip breadsticks into remaining juice mixture. Turn each breadstick 2 or 3 times allowing it to absorb some of the juice mixture. Don't allow them to become soggy. Use enough breadsticks to cover fruit mixture. Pour any remaining juice mixture over bread and fruit.
Sprinkle topping mixture over everything. Bake at 350 ° for 30-40 minutes. Cool slightly before serving.
Note: If you are using dried fruit, mix 1/2 cup dried apples and 1 to 1-1/2 cups dried, pitted pie cherries. Add about 3 cups of water. Soak overnight and/or simmer slightly to fully reconstitute fruit. Drain fruit. You should have about 10 oz. of liquid left over for recipe.