In a large bowl, whisk together heavy cream, half & half, brown sugar, and vanilla extract. Melt the peanut butter in 30-second increments in the microwave, until melty. Whisk the melted peanut butter into the liquid mixture. Add in peanut butter chips and milk chocolate chips, and stir.
Pour into your ice cream maker, and churn for about 20 minutes, or until thick and creamy.
While the ice cream is churning, mix the chocolate peanut butter, milk chocolate chips, butter, and vanilla in a microwave safe bowl. Melt in 30-second increments, until the mixture is smooth, stirring after each hit in the microwave (it only takes about 60-90 seconds, depending upon your microwave). Set aside.
Once your ice cream is ready, pour 1/3 of the ice cream mixture in a freezer-safe container. Spread half of the chocolate peanut butter swirl over the ice cream. Layer 1/3 of the ice cream on top. Spread the remaining chocolate peanut butter swirl over the ice cream. Layer the final 1/3 of ice cream over the top (when scooped, the ice cream will have a nice chocolate swirl throughout).
If you like soft-serve ice cream, eat immediately. If you prefer a firmer cream, allow to freeze for at least 2-3 hours (when frozen, allow ice cream to sit out at room temperature for about 10 minutes to soften).
Enjoy!