Stir sugar and cocoa powder together in large saucepan. Stir in milk. Heat at medium-high heat until boiling, then lower heat and let low boil continue. Stir occasionally.
Have ready a greased pie plate or similar dish. Start checking temperature with a candy thermometer when bubbles get small and glossy. (Total cooking time will be 20 minutes or less depending on amount of milk.)
Remove from heat when mixture reaches 235 F degrees or “soft ball” stage. Set pan in cold water to cool. Add vanilla extract.
Let cool slightly and add peanut butter. Remove from cold water and stir quickly to mix in peanut butter. Pour fudge into pie plate. Let cool and cut into pieces.