In a mixing bowl, beat butter with electric mixer on low speed or by hand until creamy, then blend in egg. Slowly add dry sugar cookie mix and blend until all incorporated.
Gather dough into a ball and flatten into a disc. Wrap dough in plastic and freeze 20 minutes or until firm. Preheat oven to 350 degrees and line a baking sheet with parchment paper. Remove dough from freezer and flour a flat surface. Roll out dough to 1/4" and use the clover cookie cutter to cut the dough.
Place cookies onto prepared pan. Use your fingers to round the edges of the clover leaves to create the arms of the fidget spinner. Remove the stem of the clover, then roll and flatten into a flat disc. Place the discs of dough and the fidget spinner cookies on opposite sides of the sheet pan.
Bake 5-6 minutes, then remove the circle cookies and cool on a wire rack. Continue baking fidget spinner cookies another 6-7 minutes, until golden around the edges. Remove from oven and cool 5 minutes on the sheet pan before removing to a wire rack.
To make the frosting, blend the butter and yogurt together in a medium sized bowl until smooth. Add dry frosting mix and blend until smooth and creamy, about a minute. Use the natural food dye to make the frosting any color you like. Place frosting into piping bags or a plastic storage bags.
Use a scissors to cut the end off tip, then pipe frosting onto the center of each fidget spinner cookie. Place one circle cookie onto the frosting, then use remaining frosting to decorate cookies however you like!