Preheat oven to 400 degrees. Line a large baking sheet with parchment paper.
Add butter to a small skillet. Turn the heat on medium-high and let the butter melt. Once the butter starts to turn brown, swirl the pan until it becomes a deep brown and smells nutty. Pour butter into a small bowl and place in the freezer. After about 10 minutes, check the butter, if it has solidified again, scoop onto a piece of plastic wrap and wrap up, jelly-roll style so that the butter is in a log. Place back into the freezer until chilled, about 10 more minutes. Once chilled cut into a small dice.
In a medium bowl, whisk together flour, baking powder, salt and both sugars.
Add chopped butter to the flour mixture and use a fork to cut the butter into the flour. Once the mixture resembled course meal, toss in the walnuts and the cherries.
Make a well in the center of the dry ingredients and add half and half. Use your fork to stir just until all the ingredients are combined. Pour on to a lightly floured surface and pat into a 12x3 rectangle. Cut into 8 triangles and place on prepared baking sheet. Brush with half and half and bake for 15-20 minutes or until golden brown on the edges and cooked through.
Let cool completely and sprinkle with powdered sugar right before serving.