1. FOR THE FILLING: Bring all ingredients, except for thyme, to simmer in medium saucepan over medium-high heat. Cover, reduce heat to low, and cook until apples are very soft, about 20 minutes. Push mixture through fine-mesh strainer to extract as much liquid as possible. Return liquid to saucepan and simmer over medium-high heat until reduced to 1/3 cup, about 5 minutes; reserve glaze. Meanwhile, pulse apple mixture in food processor until uniformly coarsely chopped, about fifteen 1-second pulses. Transfer apple mixture to bowl and stir in thyme; refrigerate while preparing pork.

2. FOR THE PORK: Soak wood chips in water for 30 minutes. Meanwhile, following illustrations 1 through 3 above, cut meat to even 1/2-inch thickness. Season inside liberally with salt and spread apple filling in even layer, leaving 1/2-inch border (illustration 4). Roll tightly and tie with twine at 1-inch intervals (illustrations 5 and 6). Season exterior liberally with salt and pepper.

3. Drain chips and place in small disposable aluminum pan. About 20 minutes before grilling, place pan with chips on primary burner (burner that will remain on during cooking); position cooking grate over burners. Turn all burners to high and heat with lid down for 15 minutes. Scrape and oil grate. Leave primary burner on high and turn off other burners. Place roast, fat-side up, on side opposite primary burner.

4. Grill-roast until instant-read thermometer inserted into thickest part of roast registers 130 to 135°F, 55 to 70 minutes, flipping once halfway through cooking time. Brush roast with half of reserved glaze; flip and brush with remaining glaze. (You may need to reheat glaze briefly to make spreadable.) Continue to cook until glaze is glossy and sticky, about 5 minutes longer.

5. Transfer roast to cutting board, loosely tent with foil, and let rest for 15 minutes. (Internal temperature should rise to about 145°F) Cut into 1/2-inch-thick slices, removing twine as you cut. Serve immediately.

Serves 6