In a large mixing bowl combine the flour, sugar, baking powder, and baking soda. Cut in the butter with a pastry blender. Or use the food processor in batches to cut in the butter quickly. Gently mix in the half and half, just until mixed. Fold in the berries.
On a lightly floured surface, pat dough into a 2 inch thick rectangle. Cut into 16-20 squares or triangles, depending on how big you want them. Place on a parchment- or silpat-covered tray, keeping the scones about 2 inches apart. These will spread a fair amount.
If baking right away, brush them with the extra half and half and sprinkle with the sugar. Bake for 15 to 18 minutes in preheated 400° oven. Cool slightly before serving.
Notes
If preparing ahead of time, flash freeze the scones on a lined tray. Once they are frozen solid, transfer them to a ziptop freezer bag. Bake according to directions in step 3, increasing baking time if necessary. (Baked scones can also be frozen in a ziptop freezer bag.)