Yeah. I don't have a recipe for this one either, sorry. This is the first incarnation of what will probably be many. I did it on a whim and while it was good, it wasn't... complete. Next time (probably tomorrow) I will use brown sugar instead of white and maybe some cinnamon. I'm also tempted to add a pinch of salt, to both heighten the flavor and pull out some of the juices. I have this vision of peach juice, melted brown sugar and browned butter turning into a faux caramel mixture kind of thing. I don't know if that's actually going to happen, but I'm going to try. For those of you who are keeping score at home, here is what I did.
First, I got my butter going (I used about a half tablespoon). I figured it should be just starting to brown when I put the peaches on, otherwise it runs the risk of burning. That took just a couple minutes. Then I cut a peach in half. I figure one peach is a portion (fruit is good and all), but you could do half per person and still have it be fine. I sprinkled them with some sugar and plopped them onto the pan. I used nonstick heated to medium/medium high for this. Once they had browned up I plopped some in a bowl, poured the browned butter in the convenient hollow where the pit had been and thought "This could use some ice cream". So I put some ice cream on there. It was Hagen Daaz caramelized pear and pecan. It went really well with it. I think making a reduction with the browned butter, whatever juices the peach puts out, any leftover sugar and a sweet wine would be good. More experiments are clearly needed.