In bowl, whisk together flour, cocoa and salt. In another bowl, beat butter and sugar with electric beaters until light and fluffy. Beat in dry ingredients just until blended. Stir in grated chocolate. Turn onto lightly floured surface and pat dough into 2 disks. Wrap each in plastic wrap and refrigerate at least 1 hr.
Preheat oven to 325°F (160°C). F. Line 2 baking sheets with parchment paper. One at a time, roll each dough disk between 2 large sheets of parchment paper to 1/4-in. (5-mm) thickness. With lightly floured 2-in. (5- cm) round cookie cutters, cut out circles of dough. Re-roll scraps once and cut more cookies. Make 24 cookies. Place on prepared baking sheets, spaced 1-in. (2.5 cm) apart. Chill at least 10 min. before baking.
Bake 8 to 10 min., swapping racks and rotating sheets halfway through, until bottoms of cookies are lightly golden and tops are set. Transfer cookies to wire racks to cool completely.
Meanwhile make buttercream frosting. Beat butter with electric mixer until fluffy. On low speed, beat in icing sugar, cream and vanilla until smooth. Increase speed to high; beat 1 to 2 min. until frosting is light and fluffy.
Spread frosting on each cookie. Store in airtight container for 2 to 3 days.
Garnish frosted cookies with extra grated chocolate.
For tender, buttery shortbread, do not overwork the dough. You want the butter to melt in the oven not before. If dough feels too soft at any stage, pop in freezer to firm up the dough.