Butter an 8-inch square pan or a small glass casserole dish and set it aside.

In a heavy saucepan over medium heat, combine the brown sugar, milk, and butter.

Stir steadily until the butter melts and the sugar dissolves into a smooth caramel-colored mixture.

Bring the mixture to a gentle boil and cook, stirring often, until it reaches the soft-ball stage (about 234 to 240 degrees Fahrenheit).

If you don't have a thermometer, drop a little of the mixture into cold water. It should form a soft ball that flattens when lifted.

Remove the pan from heat and stir in the vanilla.

Let the mixture cool undisturbed for 5 to 10 minutes, until it thickens slightly.

Beat the fudge with a wooden spoon until it loses some of its gloss and starts to look thicker and creamier.

Quickly spread it into the prepared pan.

Allow the fudge to cool completely, then cut it into squares and serve.

For neat pieces, let it set fully before slicing.