Add the chocolate chips and peanut butter to a microwave-safe bowl. Microwave in 30-second intervals, stirring well after each, until the mixture is completely smooth and melted.

Pour the Rice Chex cereal into the melted chocolate mixture and gently fold until every piece is evenly coated. Place the bowl in the refrigerator while you prepare the ice cream base.

In a large mixing bowl, whisk together the sweetened condensed milk, peanut butter, vanilla extract, and salt until smooth and creamy.

In a separate large bowl, beat cold heavy whipping cream with an electric mixer on medium-high speed until stiff peaks form. The whipped cream should hold its shape when you lift the beaters.

Gently fold the peanut butter mixture into the whipped cream with a rubber spatula until no streaks remain. Fold just until combined to keep the whipped cream light and airy.

Remove the cereal from the refrigerator, add the powdered sugar, and toss until every piece is evenly coated. Break up any large clusters before assembling the ice cream.

Spread half of the ice cream base into a 32-ounce deli container, loaf pan, or another freezer-safe container. Top with half of the puppy chow, then repeat with the remaining ice cream and puppy chow. Use a butter knife or skewer to gently swirl the layers together a few times to distribute the puppy chow throughout the ice cream.

Cover tightly and freeze for at least 8 hours, or overnight, until firm. Let the ice cream sit at room temperature for 10 to 15 minutes before scooping so it softens slightly and is easier to serve.