Move oven rack to the lower-middle part of the oven. Preheat oven to 400° F/240° C.
In the food processor bowl, mix the flour, sugar, baking powder, baking soda, and salt. Add the pieces of butter and pulse about 10 to 12 times. The mixture should resemble coarse cornmeal.
In a small bowl, whisk together the sour cream, egg, and almond extract until smooth.
Pour the flour mixture into the large mixing bowl and add the dried cherries. Stir in the sour cream mixture until large dough clumps form. Press it all together with your hands.
Flour your hands. Place the dough on a lightly floured surface and pat into an 8-inch circle about 3/4-inch thick. Brush cream on the top.
Cut into 8 triangles and place them on the prepared baking sheet about 1 inch apart. Sprinkle sugar on top of each. Bake until golden, about 18 to 20 minutes. Cool for 5 minutes and serve warm or at room temperature.