Preheat oven to 350°F. Line a baking sheet with parchment paper and set aside.
In a medium bowl, whisk together the flour, cornmeal, baking powder, salt and black pepper.
In a separate bowl, cream together the butter and sugar until light and fluffy. Add in the eggs, one at a time, beating well after each addition. Stir in the dry ingredients until well-combined. Fold in the corn, cheddar and jalapeño.
Transfer the mixture to the prepared baking sheet. Using floured hands, form into a log that is roughly 14 by 3 1/2 inches. Bake until firm, lightly golden brown, and slightly cracked on top, 30 to 35 minutes. Remove from the oven and let cool for 15 minutes.
Carefully transfer the log to a cutting board. Use a very sharp serrated knife, cut on a slightly diagonal into 1/2-inch thick slices. Arrange on the baking sheet, close together. Bake the biscotti for 10 minutes. Remove from the oven and carefully flip each over. Return to the oven and bake for 10 minutes longer. Allow to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely. They're crisp up and dry out slightly as they cool. Serve with honey butter or softened salted butter and a drizzle of honey. Enjoy!