Preheat Oven:
Preheat your oven to 350°F (180°C). Grease and flour a 9-by-13-inch rectangular baking dish with butter or use nonstick cooking spray.
To make the cake batter:
In a large bowl, combine the cake mix, instant pudding, oil, water, eggs, vanilla extract, and lemon zest. Mix with an electric mixer on medium speed for 2-3 minutes, until smooth and blended.
To bake the cake:
Pour the batter into the prepared pan and spread it evenly with a spatula. Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
To cool:
Remove the cake from the oven and let it cool slightly in the pan on a wire rack.
To make the lemon frosting:
In a medium bowl, combine the powdered sugar, lemon zest, melted butter, heavy cream, and half of the lemon juice. Gradually add the remaining lemon juice until desired consistency: creamy, but runny enough to coat the cake.
Cake icing:
Pour the icing over the cake while it is still warm. Use a spatula to spread the icing evenly. Allow to harden slightly before cutting and serving.
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