I did a similar booking last month, though it was a one-way from Europe to the US on UA, in economy. I had to call the Asiana service center and the total process took about 10 minutes on the phone.

Before doing so, I went on UA's site to look for award tickets, to get an idea generally of *A award availability, so I knew what to ask for when I called in. It cost a little more $-wise to use OZ vs UA miles, but not a huge difference, like $60 vs $120 as I recall.