1. Combine 2 cups flour, sugar, dry yeast and salt in a large mixer bowl and stir until blended. Combine milk, water and butter in a microwave-safe bowl. Microwave on HIGH in 15 second increments until very warm but not hot to the touch (120° to 130°F. Butter won’t melt completely). Add to flour mixture with egg. Fold in grated apple.
2. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup flour; beat 2 minutes at high speed, scraping bowl occasionally. Stir in just enough remaining flour so that the dough will form into a ball.
3. Knead on lightly floured surface until smooth and elastic and dough springs back when lightly pressed with 2 fingers, about 6 to 8 minutes. Cover with a towel; let rest for 10 minutes.
4. For filling, combine sugar, cinnamon, and allspice in a shallow bowl.
5. Cut dough into 36 pieces. Dip each piece into the melted butter and then roll in the cinnamon sugar mixture. Place in fluted tube pan that has been generously sprayed with cooking spray. Combine any remaining butter and sugar and drizzle over rolls. Cover with towel; let rise in warm place until doubled in size, about 45 minutes .
6. Bake in preheated 375ºF oven for 25 to 30 minutes or until rolls are golden brown. Cool 5 minutes in pan, then invert on serving plate.

For the Apple Cider Glaze

1. In a small saucepan, melt butter over medium heat. Whisk in apple cider, heavy cream, and salt. Bring the mixture to a gentle simmer, and then remove from the heat. Whisk in powdered sugar. Allow to cool slightly before pouring over the pull apart bread.