In a large bowl, whisk together the flour, cornmeal, granulated sugar, rosemary, and cayenne. Using a pastry blender or fork, cut in the butter until the mixture resembles coarse meal. (You may need to add water, 1/2 teaspoon at a time, to help the dough come together.) Stir in the dried cranberries. Form the dough into a disk, wrap in plastic wrap, and refrigerate for at least 1 hour.
When ready to bake, preheat the oven to 325°F and line the baking sheets with parchment paper. On a lightly floured surface using a lightly floured rolling pin, roll the dough to 1/4 -inch
thickness. Use cookie cutters to cut the dough and place the cookies 2 inches apart on the prepared baking sheets. Repeat with the remaining dough, gathering up scraps, re-rolling, and cutting until all the dough is used.
Bake until lightly brown, 21 to 24 minutes. Remove the cookies from the oven and cool on the baking sheets for 5 minutes. Brush the cookies with the glaze; then transfer the cookies to a wire rack to cool completely.