Adding melted butter to cold milk in baking
Melting the butter and mixing it with milk or other liquid ingredients is almost always done as part of the muffin method, where a muffin, cake or quick bread batter is formed by mixing dry ingredients together, wet ingredients together, and then quickly combining the two.

In practice, the butter is not going to mix with the milk.  It is going to mostly float on top, and stay liquid.   You will have sufficient time to combine the wet and dry mixes, and create the batter.

Putting them together just makes it easier to form the final batter.  It would work just as well if you made a dry mix, then added the remaining liquid ingredients (usually milk, eggs, and maybe some flavoring), and then the melted butter.  When you stir the dry and wet mixes together, the butter is going to become fairly uniformly mixed into the batter.

Note that many quick breads are made with oil, which is treated the exact same way, even though melting is not an issue.  The only reason to use butter is because the flavor is desired for whatever item is being made.