Beat butter at medium speed with an electric mixer until creamy. Gradually add 3/4 cup powdered sugar, beating until smooth. Stir in 3/4 cup canned sweet potato puree and 2 tsp. vanilla until blended.
Stir together flour and next 6 ingredients. Gradually add flour mixture to butter mixture, beating at low speed until blended.
Divide dough in half; flatten each into a disk. Roll each disk to 1/4-inch thickness between 2 sheets of wax paper. Transfer dough, in wax paper, to a baking sheet; chill 1 hour.
Preheat oven to 350°. Working with 1 portion of dough at a time, remove top wax paper; cut with a 2-inch round cutter, rerolling dough scraps once. Place 1 inch apart on parchment paper-lined baking sheets; sprinkle with Demerara sugar.
Bake at 350° for 12 to 14 minutes or until edges are golden. Cool on baking sheets 1 minute; transfer to wire racks. Cool completely.
Beat marshmallow crème and softened butter with a heavy-duty electric stand mixer at medium speed 2 minutes or until smooth; gradually add 2 cups powdered sugar. Add meringue powder, and beat at high speed 2 minutes or until fluffy. Stir in 1 tsp. vanilla extract. Spread about 2 tsp. mixture between cooled shortbread rounds to form sandwiches. Store in airtight containers.