Preheat your oven using the instructions on your brownie box for a 8x8 or 9x9 pan.
Make your brownie batter and pour into a prepared pan.
Over a double boiler, melt your 1 cup of white chocolate peppermint chunks. *To make a double boiler, in a small pot add about an inch of water. Place a heat-safe bowl over the pot so that it doesn't tough the water or bottom of the pot. Add your chocolate into the bowl. Turn your stove to medium high heat and let the steam from the water slowly melt the chocolate, stirring occasionally. Be careful, your bowl will get warm, use a towel or oven mitten to help hold it as your stir the chocolate until it melts.
Pour the melted while chocolate over the brownie batter. To make a swirl pattern, pour the melted chocolate in about 4 vertical lines - in the same direction. Using a knife or toothpick gently make lines in the opposite direction so that it drags the white chocolate into a swirl-like pattern.
Bake according to your brownie box instructions for a 8x8 or 9x9 pan.