In a large bowl, combine the marshmallow creme, 1 tablespoon milk and vanilla. Gradually beat in confectioners' sugar until combined. With lightly greased hands, shape the mixture into 1-1/2-in. x 3/4-in. logs. Place on a waxed paper-lined baking sheet. Freeze for 3-4 hours or until firm.
Place the caramels and remaining milk in a microwave-safe bowl. Microwave, uncovered, at 70% power for 1 minute. Stir; heat 1 to 1-1/2 minutes longer or until mixture is melted and blended.
Remove four logs from the freezer at a time. Pierce with a meat fork and spoon caramel over all sides. Shake or scrape off excess caramel. Immediately roll in peanuts. Place on waxed paper. Repeat with remaining logs. Reheat caramel in the microwave for 15 seconds as needed. Store in an airtight container in the refrigerator.