Line three large baking pans with parchment paper or lightly grease with cooking spray.
In a large bowl, beat the butter, brown sugar, and granulated sugar with an electric hand mixer or stand mixer with fitted paddle attachment until light and fluffy, about 2-3 minutes.
Add pudding mix, eggs, vanilla and peppermint extracts, beating well. Add the flour, ½ cup at a time, followed by baking soda and salt. Mix until combined. Gently fold in chocolate chips and candy cane pieces.
Chill dough in refrigerator for 30 minutes to 1 hour, if desired. This will help the cookies to bake up soft and round, rather than spread out.
Preheat oven to 375°F. Using a cookie scoop or spoon, scoop dough into balls about 2 tablespoons each and place onto prepared baking pans. **To avoid having the candy cane pieces melt onto your baking pan, make sure the dough covers the pieces before baking. When you remove from the oven, you can press candy cane pieces into the top for more texture, if desired.**
Bake for 11-15 minutes, or until golden brown around edges of cookie. Remove from oven and allow cookies to cool on baking pan for 10 minutes. Then remove to a wire rack to cool completely.