Stir together chili-lime rub, brown sugar, lime zest, and ½ teaspoon salt in a small bowl. Sprinkle and rub mixture over all sides of pork. Let stand at room temperature for 30 minutes.

Heat oil in medium skillet over high heat. Add pork; cook for 3 to 4 minutes on each side or until lightly browned on all sides, turning frequently. Set pork aside.

Place sweet potatoes, apples, and broth in a 6-quart slow cooker. Place pork roast on top. Stir together ½ cup apple butter, honey, lime juice, 1 tablespoon cilantro, and remaining ½ teaspoon salt in small bowl; pour over pork. Cover and cook on high for 2 to 2½ hours or low for 4 to 5 hours or until pork reaches 145°.

For purée, transfer 3 cups of cooked apples and sweet potatoes to a food processor. Add remaining ½ cup apple butter. Cover and pulse until smooth. Garnish pork with additional cilantro, if desired.

To serve, slice pork; serve with purée and remaining cooked apples and sweet potatoes. If desired, drizzle with cooking liquid.