Preheat your oven to 350°F (175°C).
Prepare the brownie mix according to the package instructions, adding the vegetable oil and eggs, along with the peppermint extract.
Spread half of the brownie batter onto a greased baking pan, pressing it evenly into the corners.
In a separate bowl, mix together the softened cream cheese, powdered sugar, and crushed candy canes until smooth.
Spoon the cream cheese mixture evenly over the brownie base and smooth it out.
Top the cream cheese layer with the remaining brownie batter, spreading it gently over the filling.
Bake in the preheated oven for 25–30 minutes, or until a toothpick inserted comes out mostly clean.
Remove the brownies from the oven and let them cool completely in the pan.
Once cooled, cut into squares and dip the tops in melted chocolate, then sprinkle with additional crushed candy canes.