In a saucepan over medium heat, melt butter, then stir in brown sugar and sweetened condensed milk until everything combines into a smooth, glossy mixture.
Keep stirring constantly as the caramel gently bubbles and thickens, watching the color deepen from pale gold to rich amber.
Remove from heat, stir in vanilla extract, then immediately pour into a parchment-lined square pan and spread evenly with a spatula.
Refrigerate for at least 2 hours until completely firm, then lift out using the parchment, slice into squares, and serve.
