Line a jelly roll pan with heavy-duty foil (heavy-duty foil is essential!), extending the foil over the edges of the pan. Butter the foil and set the pan aside.
In a heavy 6-quart pot, melt butter over medium-low heat then add the brown sugar, condensed milk, and corn syrup; mix well.
Cook and stir over medium-high heat to boiling.
Clip a candy thermometer to side of pan. DO NOT touch the thermometer to the bottom of the pot.
Cook and stir over medium heat to 248°, firm-ball stage.
Remove pot from heat, remove the thermometer, and stir in the vanilla. Immediately pour the mixture into your prepared pan. Allow to set overnight.
The next day, when caramel is set, use foil to lift out of pan. Cut the caramel into 1-inch squares with a sharp, buttered knife. Wrap each piece in a 3×3″ square of waxed paper.