For the scones:
For the glaze:
Preheat the oven to 400˚ F. Line baking sheets with silicone baking mats or parchment paper. In a large bowl, combine the flours, sugar, baking powder, cinnamon, salt and nutmeg. Whisk to blend. Stir in the pieces of cold butter and cut into the dry ingredients using a pastry cutter or two knives until the mixture resembles coarse meal and the largest pieces of butter are the size of peas.
In a second bowl, combine the mashed banana and yogurt and stir to blend. Add the banana mixture to the bowl with the dry ingredients. Fold together gently with a spatula until a dough begins to come together. (Be careful not to over mix, as it will result in tough, dense scones.) If some of the dry ingredients are not incorporating into the dough, add a bit of buttermilk 1 tablespoon at a time just until all dry ingredients are moistened and incorporated.
Turn the dough out onto a lightly floured work surface. Gently knead a few times to ensure even mixing. Pat the dough out into a slab about ¾- to 1-inch thick. Cut out rounds of dough using biscuit cutters (about 3½ inch diameter for large scones or 2½ inch diameter for smaller scones). Place the dough rounds on the prepared baking sheet at least an inch or two apart. Lightly brush the tops of the scones with buttermilk.**
Bake the scones, rotating the pans halfway through baking, until the tops are golden brown and the scones are just set, about 16-18 minutes total for large scones (slightly less for smaller scones). Let cool on a wire rack.
While the scones are cooling, make the glaze. Heat the butter in a small skillet over medium heat. Let melt and continue to cook, swirling occasionally, until the butter is a deep golden brown color (be careful not to burn it). Set aside to cool slightly. Transfer the browned butter to a bowl and whisk in the confectioners’ sugar. Whisk in the milk until the mixture is smooth. (Note: If the browned butter begins to cool, particularly if the milk is cold when added, the glaze may become very thick or difficult to whisk. Simply rewarm in the microwave in very short few-second bursts until the texture has corrected. If the mixture is too thin, whisk in additional confectioners’ sugar a small amount at a time until thickened to your liking.) Spoon or drizzle the glaze over the scones and let set before serving.
*I prefer to use half white whole wheat flour in nearly all baked goods we eat for breakfast, but you can use all all-purpose flour if you wish.
**At this point you can place the unbaked scones on a baking sheet, transfer to the freezer and freeze until solid. Then store in an air-tight freezer container and save for later. To bake after freezing, just bake as normal but add a few minutes onto the bake time and check to be sure they are fully baked through.