Dandy Cocktail

Ingredients

• 1 cup ice cubes, or as desired
• 1 (1.5 fluid ounce) jigger bourbon whiskey
• 1 (1.5 fluid ounce) jigger herbal red wine (such as Dubonnet(R))
• 1/2 fluid ounce orange-flavored liqueur (such as Cointreau(R))
• 1 dash bitters (such as Angostura(R))
• 1 (1 1/2 inch) piece lemon peel, or more to taste
• 1 (1 inch) piece orange peel, or more to taste