Place 4 full sized candy canes (broken into pieces) in food processor, and pulse until crushed, about 5 pulses. Alternatively, place the candy cans in a large zipper bag, and crush them with a rolling pin. Mix with ¼ cup granulated sugar and spread onto a plate. Set aside
Stir together 2 cups all-purpose flour, 1 teaspoon salt, and ½ teaspoon baking powder in a small bowl. Set aside.
Cream 1 cup (2 sticks) unsalted butter, remaining 1 cup granulated sugar, and 1 Tablespoon light brown sugar together using a stand mixer at medium-high speed until light and fluffy, about 5 minutes. Add 1 large eggand 2 teaspoons vanilla. Mix until well combined. Stir in flour mixture at low speed until dough forms.
Scoop 1 tablespoon portions of dough and form into balls. Roll dough balls into candy cane-sugar mixture until fully covered. Refrigerate dough balls until firm, at least one hour.
Heat oven to 375°F, with the racks at the upper-middle and lower-middle positions. Line 2 baking sheets with parchment paper or silicone baking mats (NOTE: Cookies made on silicone mats will spread more than those baked on parchment). Set aside.
Place balls onto prepared baking sheet about 2" apart. Slightly flatten balls with the palm of your hand or bottom of a drinking glass.
Bake for 12-15 minutes, until edges are just starting to brown. Don't overbake.
Remove sheets from oven, and let cool on sheet for 5 minutes. Transfer to cooling racks to cool completely. Store in an airtight container at room temperature or freeze. Candy cane coated dough balls could also be frozen and baked later.