In a heavy saucepan, melt butter over medium heat just until it becomes fragrant and starts to turn brown. Or just melt it. You don't have to brown it. Turn off heat (or remove from heat if using an electric stove) and pour butter in a small cup set next to stove.
In the same saucepan, combine all of the dry ingredients. Turn heat back to medium and gradually whisk in the milk. Bring to a full boil over medium heat. Leave at a gentle boil, whisking or constantly for about 2 minutes .
Turn off the heat and add the melted butter and vanilla.
Pour into a bowl or 3 individual bowls. Let cool for about 30 minutes at room temperature, then transfer to the refrigerator to chill.
Notes
You can skip the step of browning the butter and just add thin slices of butter at the end.