In a large bowl, combine flour, sugar, baking powder, and salt, whisking well. Using a pastry blender, cut butter into flour mixture until it resembles coarse crumbs. Add apricots, stirring to combine.
In a liquid-measuring cup, combine sour cream, 6 tablespoons whipping cream, and vanilla extract, stirring to blend. Add to flour mixture, stirring until mixture is evenly moist. (If dough seems dry, add more cream, 1 tablespoon at a time.) Working gently, bring mixture together with hands until a dough forms.
Turn out dough onto a lightly floured surface. Knead gently 4 to 5 times. Using a rolling pin, roll dough to a ½-inch thickness. Using a 2-inch fluted round cutter, cut 20 scones from dough. Place scones 2 inches apart on prepared baking sheet.
Brush tops of scones with remaining 1 tablespoon cream.
Bake until edges of scones are light golden brown and a wooden pick inserted in the centers comes out clean, approximately 18 minutes.