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1
Preheat oven to 350. Prepare 2 round cake pans (9 inch) by greasing and flouring lightly. You could alternately grease and line with parchment paper.
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2
Use double-layers of paper towels in batches to squeeze out some extra moisture from the grated squash. In a large bowl, combine lemon zest, juice, eggs, oil, and vanilla. Once mixed well, add in squash. In a separate bowl, whisk together the flour, cornmeal, sugar, baking powder, baking soda and salt.
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3
Add your wet ingredients to the dry, and stir until combined. Pour evenly into your two prepared pans, smooth tops as needed, and bake on center rack of oven for 35 to 40 minutes, or until an inserted toothpick comes out clean.
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4
Let cool on a wire rack. After 15 minutes, run a knife along the inside pan edge to loosen and invert cakes onto a plate to remove pans, then invert again onto racks. Allow to cool completely before frosting.
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5
To make your frosting, add your butter to the bowl of a stand mixer fitted with the paddle attachment. Beat until smooth and creamy. With the mixer on a low speed, gradually add in your sugar, stopping occasionally to scrape down the sides. Add in 2 tablespoons milk, pepper, and scrape in the vanilla seeds and beat to combine. Turn speed to high and beat until fluffy, up to 5 minutes. If the frosting seems too stiff, add remaining milk incrementally until you reach your desired consistency.
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6
To assemble cake, place one layer top-side down on a cake stand. Ice on top of this (about a half cup) and smooth. Place second layer, top side down, on top of this. Ice top of cake, and then sides. Smooth with a offset spatula.
