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