1. Heat oven to 375 degrees. In an 8-by-8-inch baking dish, toss cranberries with cornstarch, 1/2 teaspoon cinnamon, and 1/4 teaspoon salt. Drizzle with 1/4 cup honey. Arrange apples on top of cranberries in one layer, skin sides down. Drizzle with 3 tablespoons honey. Sprinkle with 1/4 teaspoon cinnamon and 1/4 teaspoon salt.

2. Melt together butter, remaining honey, and remaining 1/4 teaspoon cinnamon. Working with one sheet of phyllo at a time and keeping the others covered with plastic wrap, brush very lightly with butter mixture. Lay a second sheet over first and brush with butter mixture. Repeat with one more sheet. Tear the phyllo crosswise into 4 pieces, and loosely crumple (as you would a tissue) as you place on top of the apples. Repeat with remaining three sheets of phyllo and butter mixture.

3. Bake for 20 minutes, then reduce to 350 degrees. Bake until juices bubble in center and apples are tender, 40 to 50 minutes more. If top darkens too quickly, tent with foil. Cool 30 minutes.