The process of mixing butter and sugar is called 'creaming' and the purpose is "Creaming adds air. Air is fluffy." so you are on the right track, but unlikely to get consistency out of just using 'melted butter'. The creaming process is time sensitive, that is, the more you do it, the more 'cake like' your cookies will be. Rather than using melted butter, which will not mix well with your sugar, just cream for a shorter period of time. In this picture you see the results of creaming over time...   You are probably looking to only reach #3 or #4 to consistently get the results you seek. (Have fun experimenting to get it 'just right')

The process of mixing butter and sugar is called 'creaming' and the purpose is "Creaming adds air. Air is fluffy." so you are on the right track, but unlikely to get consistency out of just using 'melted butter'. The creaming process is time sensitive, that is, the more you do it, the more 'cake like' your cookies will be. Rather than using melted butter, which will not mix well with your sugar, just cream for a shorter period of time. In this picture you see the results of creaming over time...

These are from the linked article [above] showing minute-by-minute progress of creamed butter, with the egg added in the last stage.

You are probably looking to only reach #3 or #4 to consistently get the results you seek. (Have fun experimenting to get it 'just right')