In a mixing bowl, combine the creamy peanut butter and softened vanilla ice cream. Use a spatula to mix them together until smooth and well combined.
Take one Ritz cracker, and spread a generous amount of the peanut butter and ice cream mixture on top. Place another Ritz cracker on top to create a sandwich. Repeat this process until you have made 12 sandwiches.
Cover the baking sheet with plastic wrap and place it in the freezer. Allow the sandwiches to freeze for at least 1-2 hours, or until the ice cream is firm.
While the sandwiches are freezing, melt the milk chocolate chips in a microwave-safe bowl. Heat in 30-second intervals, stirring in between, until the chocolate is completely smooth.
Once the sandwiches are frozen, dip them into the melted chocolate using a fork. Allow any excess chocolate to drip off, then place them back on the baking sheet.