In a cocktail shaker, muddle grilled apple slices. Add ice, bourbon, ginger liqueur, the grilled-apple juice, lemon juice, and bitters. Shake vigorously until cold. Pour through a fine-mesh strainer and into a rocks glass with ice. Garnish with a cinnamon stick and a grilled apple wedge. The strainer helps keep the cocktail as clear as possible since there’s a lot of pulp in the apples and in the cocktail shaker.