Mix the dough:
In a small saucepan, heat the orange juice until very hot. Add the cran-berries; let steep off the heat until softened, about 15 min. Drain the cranberries, pat dry on paper towels, and coarsely chop into 1/4-inch pieces.
Put the oatmeal in a food processor and pulse eight to ten times to just break up the oatmeal. Remove 1/2 cup and transfer to a long shallow pan (like a 7x11-inch Pyrex dish). Add the flour, cinnamon, baking soda, and salt to the food processor and pulse with the remaining oatmeal eight to ten times just to blend the ingredients. Don't overprocess; the oatmeal should remain coarse.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and orange zest on medium low until well blended, about 2 min. Add both sugars and mix for another 2 min. Blend in the egg and vanilla, scraping the bowl as needed. Reduce the mixer speed to low. Add half of the dry ingredients, then the cranberries, and then the remaining dry ingredients. Mix just until combined.
Shape the dough:
Have ready six 15-inch sheets of plastic wrap. Portion the dough into thirds. Drop spoonfuls of dough onto each sheet and use the plastic to roll and shape the dough into logs about 8 inches long. Refrigerate the dough to firm it slightly, about 30 min. When chilled, roll one log at a time in the reserved oatmeal. Reroll each log tightly in a clean sheet of plastic wrap, twisting the ends firmly to seal. With your hands at either end of the log, push firmly toward the center to compact the log so it measures about 7 inches long and 1-1/2 inches thick. Refrigerate the logs until firm enough to slice (they must be very well chilled), about 4 hours, or freeze for up to three months.
Bake the cookies:
Position racks in the upper and lower thirds of the oven. Heat the oven to 350°F. Line two rimmed baking sheets with parchment. Working with one log at a time, use a tomato knife or other small serrated knife to slice the dough into 1/4-inch-thick rounds, using a gentle sawing motion. Set the rounds 1 inch apart on the prepared pans. Bake the cookies until set on top and lightly browned around the edges, about 15 min., rotating the pans as needed for even browning. Let cool on the sheets for about 5 min. before transferring the cookies to racks. When cool, store between sheets of waxed paper in an airtight container for up to a week, or freeze for up to three months.