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1
Heat the oven to 350 degrees. Melt the butter in a small saucepan over low heat, then remove from the heat and stir in the zest of one lime. Set aside to cool.
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2
In a large bowl, stir together the flour, cornmeal, salt, sugar and baking soda. (You may want to use an electric mixer on low speed for the next few steps.)
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3
Stir in two of the eggs, one at a time, mixing thoroughly after each addition. Add the cooled butter and combine thoroughly. Let the dough sit for a few minutes.
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4
Line two cookie sheets with parchment. Divide the dough in half, and with wet hands, mold each half into a long, thin log about 1 inch wide. Place one log in the center of each cookie sheet (the dough will spread significantly while cooking).
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5
Lightly beat the remaining egg with a tablespoon of water. Brush the top and sides of each log with the egg and bake until golden brown, 20-30 minutes. Let the logs cool on a wire rack for at least 30 minutes, and lower the oven heat to 200 degrees.
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6
Using a serrated knife, cut the logs on the diagonal into 1/4-inch slices. Arrange the slices on the parchment-lined cookie sheets and bake for about an hour, until crisp. Cool completely on wire racks before making the glaze.
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7
For the glaze, stir together the zest of the second lime, the confectioners' sugar and the lime juice. Drizzle this over the biscotti while it is liquid (it will start to crust if you let it sit for too long).
