Combine the flour, baking powder, baking sod and salt in a medium bowl and mix to combine. Set aside.

In a large bowl (or the bowl of a stand mixer) beat the butter and sugar until it is fluffy. Add the eggs, one at a time, scraping down the sides of the bowl as needed.  Add the sour cream and the peppermint extract, mix well.  Gradually start adding the dry ingredients, beating just until combined.

Divide the mixture in half and wrap each half in plastic wrap. Refrigerate 2 hours, or overnight.

Preheat the oven to 425ºF. Line baking sheets with parchment paper or silicone mats.

Lightly flour a workspace, then turn out one half of the dough onto the counter. Roll the dough to a 1/4-inch thickness. Dough will be a little bit sticky, so use flour as needed to avoid sticking.

Use a 3-inch round cookie cutter to cut out circles and transfer to prepared baking sheets. Bake the cookies just until set, and still pale, about 7 minutes. Transfer to a cooling rack or to a piece of waxed paper on the counter to cool completely.

To make the frosting, beat the butter in a large bowl until soft and fluffy. Add the peppermint extract. Start adding in the powdered sugar, 1/2 cup at a time, and beat until completely combined. Add the salt and the cream and beat until light and fluffy.

Frost each cookie and top with crushed candy canes.