Preheat oven to 350. Line a baking sheet with parchment paper.
In the bowl of a stand mixer, cream butter and sugars until light and airy (at least 3 minutes). Add in vanilla. Mix briefly. Add in eggs, one at a time, mixing briefly in between.
Sprinkle baking powder over top of mixture.
Add flour and mix in alternating amounts, starting and ending with flour:
1 c. flour. Mix.
2 tbsp. milk. Mix.
1 c. flour. Mix.
2 tbsp. milk. Mix.
1 1/2 c. flour. Mix.
Gently stir in white chocolate chips and peppermint bark chunks.
Scoop dough onto baking pan in 2 tbsp portions, spaced about 2 inches apart. Bake 9-11 minutes. Cookies should look slightly underdone. They will finish baking while cooling.
Let cool completely. Melt almond bark coating in microwave or over stovetop. Dip half of each cookie into coating, then roll in crushed cane cane pieces. Lay on parchment paper until hard.