Can (how do) you make basil essence from stems?

I work in a greenhouse harvesting produce for local restaurants and produce shops. Me and my boss pick basil every Thursday afternoon for selling on Friday mornings, but instead of selling whole stemmed basil (leaves, flowers, stems all in one), we clip all the good leaves off and sell 'em just the basil leaves by the pound. So what we're left with is lots (I mean lots) of stems and flowers and bad leaves. I was wondering if there was a way to take just the stems ('cuz they've still got some basil oil in it) and press in some sort of process to extract the oils/essences from it? My boss would prefer if we didn't use a carrier oil, but I'm not sure if it's possible to do without a carrier oil. He was thinkin' more of a pressing, then filtering and refining of said pressing. The reason for this is because lots of restaurants have expressed interest in basil essence without an oil that might add an unwanted taste (to be as neutral as possible, straight up basil). Worst case scenario, would safflower oil be a neutral enough carrier oil if one is required?