Line an 8x8x2-inch baking pan with foil; extend foil over edges. Butter foil; set aside.
Butter sides of a heavy 3-quart saucepan. Add sugar, evaporated milk, and butter. Clip a candy thermometer to side of pan. Cook and stir over medium-high heat to 236 degree F, soft-ball stage (about 12 minutes).
Remove saucepan from heat; remove thermometer. Add peanut butter pieces, marshmallow creme, peanuts, and vanilla; stir till peanut butter pieces are melted. Spread into prepared pan. Score into 36 squares while warm. When firm, cut into squares. Cool completely and wrap with plastic wrap. Store in the refrigerator. Makes about 3-1/3 pounds (36 servings).
Refrigerate 2 to 3 weeks or freeze up to 1 year.