I highly recommend baking your own brownies. Keep them somewhat gooey and break them apart into big chunks. The giant brownie chunks are the best part.
I used peppermint extract to flavor the ice cream. This one is from Whole Foods, but I'm sure you could get it almost anywhere.
1 1/2 cups whole milk
1/2 cup sugar
5 egg yolks
1 1/2 cups heavy cream
2 teaspoons peppermint extract
2 cups large brownie chunks
Combine milk and sugar in a saucepan on medium heat. Stir to dissolve the sugar. In a separate bowl, whip egg yolks. Just as the milk begins to simmer, add about half the mixture to the bowl of egg yolks half a cup at a time, stirring constantly. Slowly pour the egg yolk mixture back into the saucepan, stirring constantly. Keep stirring until a thick custard forms, coating the back of a spoon. Remove from heat, and pour custard in a separate bowl. Stir in cream and peppermint extract. Chill using an ice bath or refrigeration. If you've made brownies, break them into chunks and make sure they are cool. When cold, add ice cream mix into ice maker and churn. When it's thickened, hand stir the brownie chunks into the ice cream.