Root Beer Cake - Asian Recipe

Ingredients

• 1 tablespoon unsalted butter, at room temperature, for the pan
• 1 1/2 cups plus 1 tablespoon all-purpose flour
• One 12-ounce bottle (1 1/4 cups) root beer
• 1/2 cup molasses
• 1/2 teaspoon plus 1/8 teaspoon baking soda
• 3/4 cup dark brown sugar
• 1/4 cup plus 2 tablespoons vegetable oil
• 3 tablespoons plus 1 teaspoon granulated sugar
• One 1-inch piece of fresh ginger, peeled and grated on a microplane or on the finest side of a box grater (1 teaspoon)
• 2 teaspoons vanilla extract
• 1 large egg
• 1 3/4 teaspoons baking powder
• 1 1/4 teaspoons ground star anise
• 1 1/2 teaspoons ground cardamom
• 1/2 whole nutmeg, grated (or 2 teaspoons ground nutmeg)
• Finely grated zest of 2 lemons
• 1 teaspoon kosher salt
• 1/2 teaspoon fresh-ground black pepper
• 3/4 cup heavy cream
• 1 tablespoon sassafras bark (or 1/2 teaspoon sassafras extract; see Note))
• 2 cups powdered sugar
• Pinch of ground star anise
• Pinch of ground cardamom
• 1/4 teaspoon kosher salt
• 1/4 whole nutmeg, grated (or about 1 teaspoon ground nutmeg)
• Finely grated zest of 1/2 lemon