Adjust oven rack to lower-middle position and preheat oven to 400 degrees.
In a medium bowl, mix flour, 1/3 cup sugar, baking powder, baking soda and salt. Grate butter into flour mixture on the large holes of a box grater; use your fingers to work in butter (mixture should resemble coarse meal), then stir in cranberries and apricots.
In a small bowl, whisk sour cream and egg until smooth.
Using a fork, stir sour cream mixture into flour mixture until large dough clumps form. Use your hands to press the dough against the bowl into a ball. (The dough will be sticky in places, and there may not seem to be enough liquid at first, but as you press, the dough will come together.)
Place on a lightly floured surface and pat into a 7- to 8-inch circle about 3/4-inch thick. Sprinkle with remaining 1 tsp. of sugar. Use a sharp knife to cut into 8 triangles; place on a cookie sheet (preferably lined with parchment paper), about 1 inch apart. Bake until golden, about 15 to 17 minutes. Cool for 5 minutes and serve warm or at room temperature.