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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.
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Pour into your ice cream maker, and churn for about 20 minutes, or until thick and creamy.
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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.
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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).
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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).
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Enjoy!