In a food processor, combine the polenta with the butter, sugar, flour, lemon zest and salt and pulse until the mixture resembles coarse meal. Add the eggs and pulse just until the dough comes together. Transfer the dough to a bowl and refrigerate until slightly firm, about 1 hour (can be refrigerated overnight, the dough will be a bit firmer to work with).

Preheat the oven to 375 degrees F. Line several baking sheets with parchment paper. Drop slightly rounded teaspoons of the dough onto the prepared baking sheets about 2 inches apart. Bake the cookies for 15 minutes, or until golden around the edges and on the bottoms. Let the cookies cool on the sheets for 5 minutes, then transfer them to wire racks to cool completely.

The cookies can be stored in an airtight container for 1 week or frozen for 1 month.