Preheat the oven to 350 degrees and line a rimmed baking sheet with parchment paper and set aside.
Combine flour, brown sugar, cardamom, baking powder, baking soda and salt in the work bowl of a food processor. Process a few times to combine ingredients. Sprinkle half of the cold butter cubes over the top of the flour mixture and process until combined, about 6-8 pulses. Sprinkle the remaining cold butter cubes over the mixture and pulse just until these butter pieces are about the size of a pea, about 6 short pulses.
Transfer mixture to a large bowl. Whisk the buttermilk, egg and vanilla together in a liquid measuring cup. Make a well in the center of the dry ingredients and pour the buttermilk mixture in the center. Using a rubber spatula, fold everything together until a shaggy dough forms, kneading with your hands a couple of times if necessary to just bring everything together. Do not overmix.
Transfer dough to a floured work surface. Pat the dough into an 8 inch circle, dusting it with additional flour as necessary to keep it from sticking to your hands as you work.
Cut the dough into 8 wedges using a sharp knife or dough scraper. Transfer the dough wedges to the prepared baking sheet and evenly space them out so there are a couple of inches between each scone. Brush with melted butter and sprinkle generously with coarse sugar. Bake for 22-26 minutes or until golden brown. Serve warm.