Q. I've tried to melt a stick of butter in a pan and mix with sugar for a recipe. Every time I do this, the butter separates! How do I get the creamy texture that the recipe calls for without the separation?
Butter does that. It is basically an emulsion of oil and water that is, a combination of two liquids that are not inclined to go together, but are somehow coerced to do so. Melt them and you break the emulsion and the ingredients separate into fat, water, and milk solids. Now, does your recipe call for you to cream the sugar and butter together, or does it really call for you to melt the butter first?
We have written voluminously (well, three articles) on the subject of creaming butter. It is common to cream room-temperature butter rather than refrigerated butter. It is faster and a little easier on your mixer whether that's an electrical device or your forearm and a wooden spoon. But no one creams melted butter. It doesn't have enough structure to hold the sugar and all the tiny air bubbles that you are trying to create by creaming them together.
There are occasions when you melt the butter and then add sugar, as when making butterscotch, for example, but that really has nothing to do with creaming, which is what we believe your recipe is really asking for.
What is "to cream?"
How to cream butter
Mixing cookie dough/creaming butter