In the bowl of a mixer or in a large bowl with a hand mixer, cream butter and sugar on medium speed until light and fluffy, 3-4 minutes.
Add vanilla, peppermint extract, and salt and blend until combined. Mix in about ⅓ cup of the crushed candy canes.
With mixer on low, slowly add flour to bowl until well combined. Keep mixer on low and add milk to combine until dough comes together.
Remove pan with cookie crust from freezer and press cookie dough into an even layer over cookie crust.
Spread buttercream frosting over the top of the cookie dough and smooth evenly with a spatula. Sprinkle remaining crushed candy canes on top and add more sprinkles, if desired.
Place pan in fridge to chill for at least 45 minutes. Once chilled, remove bars from pan by lifting foil. Using a sharp knife, slice into squares.