Melt butter in a medium saucepan over medium-low heat.
Add the brown sugar to the melted butter and cook, stirring constantly, for 1 minute (be sure the butter and sugar are completely combined and you can't see any separated butter in the mixture).
Bring to a boil over medium heat. Continue cooking, stirring, for 2 minutes.
Add the milk and vanilla. Bring to a boil over medium heat. Continue cooking, stirring, for 3 minutes.
Remove from heat and set aside to cool. The longer it cools, the thicker it becomes. When it's at your desired consistency, drizzle over the cooled cake and serve.
Notes
This recipe is perfect for glazing 12 muffins or donuts, buns, or a bundt cake. For a larger batch, recipe can easily be doubled or tripled.
Be sure the butter and sugar are completely combined and you can’t see any separated butter in the mixture.
If the mixture looks like it’s separating during the cooling process, mix well until it comes back together.
When drizzeling cakes or desserts, place baking paper under the cake to catch any glaze that runs off the cake, then use the baking paper to drizzle on whatever remains. You won't want to waste a drop!