Chocolate Candy Cane Cake

Name: Chocolate Candy Cane Cake
Prep time: 40 min
Cook time: 30 min
Total time: 1 h 10 min
Cuisine: American
Ingredients: 1 3/4 cups all purpose flour; 3/4 cup dutch processed cocoa powder; 1 1/2 teaspoons baking powder; 1 teaspoon baking soda; 1/2 teaspoon salt; 1 1/2 cups buttermilk; 1 teaspoon vanilla extract; 1 teaspoon instant coffee granules (such as Folgers (optional)); 3/4 cup vegetable oil (or canola oil); 2 cups granulated sugar; 2 whole eggs; 1 egg white; 1 1/2 cups salted butter (softened (3 sticks, 3/4 lb)); 1 1/2 pounds powdered sugar; 1/4 teaspoon salt; 1 teaspoon peppermint extract; 1/3 cup heavy cream (or more, as needed); 6 candy canes (crushed (for garnish))