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Position oven racks in upper and lower thirds of the oven and preheat to 350 degrees F.
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Line cookie sheets with parchment paper.
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In a food processor, process the oats to a powder, about 30 seconds, then blend in the flour, sugar, cornmeal and salt.
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In a medium bowl, whisk together the butter, egg, lemon peel and vanilla.
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With the processor running, add the butter mixture and mix just until the dough comes together.
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Transfer the dough to a lightly floured surface and knead a few times.
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Form the dough into 2 disks and wrap each in plastic; refrigerate for 15 minutes.
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Roll dough to a 1/4 inch thickness and cut out shapes using a 2 inch cookie cutter.
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Transfer cookies to prepared cookie sheet and bake until lightly golden, about 12 minutes.