Preheat oven to 450°.
To prepare roast, combine 1/2 cup Calvados, 1/4 cup syrup, and sage sprig in a small saucepan; bring to a boil over medium-high heat. Reduce heat; simmer 5 minutes or until slightly thick. Remove from heat; discard sage sprig.
Lightly coat roast with cooking spray; rub 1 1/2 teaspoons salt and pepper over roast. Place roast on a broiler pan coated with cooking spray. Brush one-fourth of glaze over roast. Bake at 450° for 25 minutes or until browned.
Reduce oven temperature to 300° (do not remove roast from oven); bake at 300° for 1 hour and 45 minutes, brushing with glaze every 30 minutes. (Cover bones with foil if they start to become too brown).
Increase oven temperature to 400° (do not remove roast from oven); cook an additional 25 minutes or until a thermometer inserted in meaty part of roast registers 150°. Remove roast from oven; let stand 20 minutes before carving.
To prepare puree, while roast bakes, combine apple, chestnuts, 1/2 cup Calvados, sugar, and 2 tablespoons syrup in a medium saucepan; bring to a boil. Reduce heat, and simmer 15 minutes or until apple is tender. Place mixture in a food processor; add half-and-half, 2 tablespoons Calvados, 1/2 teaspoon salt, and chopped sage. Process 1 minute or until smooth.
Slice vertically between each rib bone. Serve pork with puree.
Wine note: A dish with flavors as complex as this deserves an equally complex wine. With its earthy character, pinot noir is a great foil to maple and chestnut flavors. Plus, compared to other reds, pinot noir has good underlying acidity to balance the richness of roast pork. One of my favorite moderately priced examples is the 2001 Thomas Fogarty Pinot Noir ($25) from the Santa Cruz Mountains of California. -Karen MacNeil