Pulse flour and next 3 ingredients in a food processor 7 or 8 times or until mixture is crumbly. Add egg, and pulse 4 or 5 times until dough forms. Divide dough into 7 equal portions, shaping each portion into a ball.
Roll each ball to a 9-inch circle on inverted greased 9-inch cakepans covered with parchment paper.
Bake, in batches, at 350° for 10 to 12 minutes or until golden. Cool on pans.
Beat sour cream and next 3 ingredients at medium speed with an electric mixer until combined; chill.
Process preserves in a food processor until smooth.
Spread 6 cookie layers alternately with about 3 tablespoons sour cream mixture and 3 tablespoons apricot preserves; stack. Top with remaining cookie layer; chill 8 hours. Sprinkle top with powdered sugar, if desired; pipe whipped cream around outer edge, if desired.