Vegan Vanilla Cake with Cookies-n-Cream Frosting

Ingredients

• 1 cup vegan butter, at room temperature, cubed
• 2 cups powdered sugar
• 2 tablespoons vanilla bean paste
• 3 cups all-purpose flour
• ¼ cup cornstarch
• 2 tablespoons baking powder
• ½ teaspoon baking soda
• ¼ teaspoon salt
• 2 ½ cups soy milk, at room temperature, or more as needed
• 2 tablespoons white vinegar
• 2 tablespoons vegetable oil
• ½ cup vegetable shortening, at room temperature
• ½ cup vegan butter, at room temperature
• 1 tablespoon vanilla bean paste
• 5 cups powdered sugar, sifted
• 3 tablespoons soy milk, or more as needed
• 1 cup crushed vegan chocolate cookies