Whisk the flour and baking powder together in a large bowl.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl with a hand mixer, beat the butter and sugar on medium speed until smooth (about 2½ minutes).
Beat in the eggs one at a time, scraping down the bowl as needed. Beat in the vanilla and almond extract until fluffy (about 1 minute).
Turn the mixer to low speed and add the flour mixture, a quarter at a time. Scrape the sides of the bowl after each addition. Add in your crushed candy canes and mix until just combined. The dough will form a ball around the paddle attachment and feel soft, but not sticky.
Remove dough onto a lightly floured surface and roll until it is ¼ inch thick. Wrap the dough tightly in plastic wrap and chill for 30 minutes or up to 7 days.
Preheat the oven to 375°F. Remove dough from the refrigerator and begin cutting our your candy canes using a cookie cutter. Arrange cookies on a baking sheet about ¾ inches apart.
Bake one sheet at a time on the middle rack for 7-8 minutes until puffy. Remove cookies from the oven to cool in the pan for 2 minutes, then remove to a wire rack to finish cooling.
While cookies are cooling, roughly chop the white chocolate bars into chunks. In a saucepan over low heat, melt the white chocolate. Stir frequently and be sure to watch so that it doesn't burn.
Dip the end of each cooled candy cane cookie in melted white chocolate and then either sprinkle crushed candy canes on top or roll the dipped cookie in the crushed candy canes in a shallow bowl or on a plate.
Let the white chocolate on the cookies set (I like to let them rest on wax paper so they don't get stuck!). Enjoy!