Help me, Bloggy-wan Kenobi...

Okay, time for one of those routine little questions that probably has an obvious answer, but I don't know what it is.

So I made steak for us the other day. The plan had been to do it on the grill, but the gas supply had other ideas, so I did it stovetop. All of which was fine, but the aftermath is giving me problems.

I did the steaks in one of my good anodized-aluminum pans (*not* nonstick), and I suspect there was a bit of residual vegetable oil in it from the onions I had sauteed just before the steak. I did a hot, fast sear of the steaks, maybe four minutes at Hotter Than the Blazes of Hell. And now there is this sticky, gunky crud around the edge of the pan, which I am having a damnable time getting off.

Ideas? Jane always used to deal with the dishes, so I'm missing some clues here. I'm always cautious about resorting to serious abrasives, but I don't know if there are any decent alternatives...