Melt the butter in a 3-quart heavy saucepan over medium heat. Add 1/4 cup evaporated milk and brown sugar, stirring constantly; cook 2 minutes. Bring to a boil, and cook 30 seconds. Remove from heat.
Heat 1% milk in a heavy saucepan over medium-high heat; cook until tiny bubbles form around edge (do not boil). Remove from heat.
Combine 3/4 cup evaporated milk, cornstarch, salt, and egg yolks in a medium bowl; stir well with a whisk. Gradually add hot milk. Stir hot milk mixture into brown sugar mixture. Cook over medium heat until mixture comes to a boil, stirring constantly; cook 1 minute. Remove from heat; stir in vanilla.
Spoon 1/2 cup pudding into each of 6 (6-ounce) ramekins. Cover surface of pudding with plastic wrap; chill 3 hours or until pudding is set.