Preheat your oven to 350 degrees Fahrenheit. Line an 8×8 inch square baking pan with parchment paper, leaving a little overhang on the sides to make it easy to lift the brownies out later. Lightly grease any exposed pan surfaces with a bit of butter or oil.
In a large mixing bowl, combine the melted butter and granulated sugar. Whisk them together vigorously for about a minute until the mixture looks smooth and well combined. This helps create that sought-after crackly top on the finished brownies.
Add the eggs one at a time, beating well after each addition. Stir in the alcohol-free vanilla extract and the peppermint extract. The batter should look glossy and pale at this stage.
Sift in the cocoa powder, flour, and salt. Use a spatula to gently fold the dry ingredients into the wet mixture. Be careful not to overmix, as this can make the brownies tough. Stop just when the last streaks of flour disappear, then fold in the chocolate chips.
Pour the batter into the prepared baking pan and spread it evenly with a spatula. Place it in the center of the oven and bake for 25 to 30 minutes. You want the edges to be set, but the center should still have a very slight jiggle when the pan is moved.
As soon as you remove the brownies from the oven, sprinkle the crushed candy canes evenly over the top. The residual heat will help the candy pieces stick to the surface without melting them completely. Allow the brownies to cool completely in the pan before slicing.