Preheat the oven to 425 degrees F. Line a baking sheet with parchment paper.
Place the cranberries in a food processor. Set aside to partially thaw while measuring out the remaining ingredients, approximately 5 minutes.
In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, and salt. Add the orange zest. Using clean hands, press the zest into the flour mixture to break up any clumps. Whisk to incorporate evenly.
Pulse the cranberries in the food processor until coarsely chopped. Some larger, halved pieces are fine.
Add the butter pieces to the flour mixture and use your fingers to work the butter into the dry ingredients until the mixture resembles coarse cornmeal with a few larger pieces. Stir in the cranberries until the are evenly coated with flour. Gently stir in the goat cheese, taking care not to break up the crumbles.
Combine the half & half with the orange juice and add to the bowl, mixing the ingredients until just combined. The mixture should be fairly dry, but the texture might vary depending on how much cranberry juice and goat cheese has incorporated into the dough. If the dough sticks to your fingers, combine in an additional 1-3 tablespoons of flour until the dough is no longer sticky.
Divide the dough in half and flatten into two round discs, about 7 inches in diameter. Cut each disc into 6 pieces. Brush melted butter on top of each piece.
Bake for 10-12 minutes, until both the tops and bottoms are golden. Serve warm or at room temperature.
Notes
Regular Chèvre goat cheese will work in this recipe, but if you can find it I highly recommend using a cranberry orange goat cheese, such as the one from Vermont Creamery. I used that one, which is slightly sweet and also includes cinnamon.I leave the butter in the refrigerator until immediately before adding it to the scone mixture.