Assemble cocktail ingredients. Place 1 cup of ice in a cocktail shaker. Pour in 1 ½ ounces of mezcal over ice, then add the 2 ounces of grapefruit juice, ½ teaspoon of ginger, ½ Grand Marnier and 2 dashes of orange bitters.
Prepare glasses. Place crushed ice into two rocks glasses.
Mix cocktail. Secure lid and cover on top of the cocktail shaker and close and shake vigorously for about 30 seconds.
Pour the cocktail over the ice, garnish with lime wedges (optional) and serve!