All of the girls I have ever met have had a brain (admittedly I didn't check - but motion and interaction strongly suggest it is the case). I have not found all of them beautiful. This suggests to me that these are not independent characteristics. If by 'brain' you mean that I find them intelligent, insightful and charming (how many other characteristics could be indicated by 'brains' - personality, cadence of voice, vocabulary, charisma...?), then I happen to find that beautiful.
There's my problem. I have an aesthetic appreciation for non-visual characteristics of other humans.
So you must mean 'beauty' to mean someone else. Visual appeal only, perhaps. Asking me to make a judgement of preference as if I were seeing someone (at at least two people if I am am to choose) through a one-way mirror in a sound-proof box. But even then, the way people move might sway me in a direction. Perhaps I need a photo. One with a neutral image. Perhaps a passport photo? This seems a bit artificial - but even then it's easier to assess scientifically than any concept of 'brains'.
The science of beauty has not concluded much in several hundred years of study. We know that across cultures, humans prefer symmetrical faces for some reason even if culturally they seem to prefer asymmetry. Also faces that approach the 'average'. As a man, I am likely to be less choosy than the average woman about these characteristics. The potential cost of a sexual relationship biologically is considerably less for me, so that makes some kind of sense. I would anticipate that women's preferences may change depending on the menstrual cycle.
I tried to construct a thought experiment to scientifically test your question, but I came up short because of the lack of definition and the difficulty in eliminating other factors. The closest I got was selecting a preference based on a pool of candidates made up of neutral unadorned passport photos and a selection of forum posts. And all that might test is my preference for human photos above and beyond the written word. All I could conclude was that my preference for a potential partner could not be created from these characteristics in isolation and I needed more input.
So, in short, humans are complicated and I don't know. Why do you ask?