Position a rack near the center of the oven and heat the oven to 425°F. Generously butter a standard 12-cup muffin tin, including the top rim, and dust the pan with flour. Tap out any excess.
Using a food processor, coarsely chop the cranberries. In a medium bowl, mix the all-purpose flour, cake flour, baking powder, ginger, baking soda, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar on medium speed until light and fluffy, about 2 min. Scrape the bowl. Beat in the eggs one at a time, mixing for at least 30 seconds at medium speed and scraping the bowl after each addition. Beat in the orange zest and vanilla. With the mixer on low speed, briefly beat in one-third of the flour mixture, then add 1/2 cup of the buttermilk; when combined, mix in another one-third of the flour; then mix in the remaining 1/2 cup buttermilk and the orange juice, and finally mix in the rest of the flour. Scrape the bowl and beat the batter just until smooth, another 10 seconds. Using a rubber spatula or a wooden spoon, fold the cranberries into the batter.
Spoon the batter evenly into the muffin tin (each cup will be quite full). Sprinkle the tops of the muffins generously with the turbinado sugar. Bake until the tops are golden and a skewer inserted an inch into the top of a muffin comes out clean, 15 to 18 min. Let the muffins cool in the pan for 5 min. and then turn them out onto a wire rack to cool completely. These muffins are best eaten the day they’re made.