Halve lemon and sprinkle cut sides with sugar.
Preheat an outdoor grill to medium heat (350 degrees F to 375 degrees F (175 degrees C to 190 degrees C)) or preheat a grill pan over medium-high heat. Grill lemon, cut sides down, until lightly charred, about 5 minutes. Let cool; juice lemon to yield ¾ ounce juice.
Fill a cocktail shaker half full with ice. Add bourbon, Aperol, amaro, and lemon juice. Cover and shake until outside of shaker is frosted, 30 seconds. Strain into a glass. Garnish with a lemon twist.