In bowl, whisk together flour, ground ginger, baking powder and salt until blended; set aside. Using electric mixer, beat butter and icing sugar until light and fluffy; beat in vanilla. Stir in flour mixture just until combined. Stir in crystallized ginger. Turn onto lightly floured work surface and pat dough into 2 disks. Wrap each disk in plastic wrap and refrigerate for at least 1 hour.
Preheat oven to 325°F (160°C). Roll each disk between 2 sheets of parchment paper to 1/4-inch (5 mm) thickness. Using lightly floured 2-inch (5 cm) round cookie cutters with fluted edges, cut out rounds from dough, rerolling scraps once to make 36 cookies. Place on 2 parchment paper–lined baking sheets, spacing 1-inch (2.5 cm) apart. Refrigerate for at least 10 minutes before baking.
Bake, in batches, for 10 to 12 minutes or until bottoms are lightly golden and tops are set. Transfer to rack; let cool completely.
Sour Cream Glaze: Meanwhile, whisk together icing sugar and sour cream until smooth.
Mash Cherry Pie Filling with potato masher until chunky. Dollop chunky cherries onto half of the cookies. Cap with remaining cookies.
Spread glaze over cookies and top each with edible flower. Let stand until glaze is set.