Knitted cuff

I have this idea of making a knitted cuff and encasing it in fabric. But I just cant see how to do it. I am now on my third attempt and I just cant make the casing professional enough. My problem is at the ends where the two pieces of fabric meet. The middle section look awesome. I have googled it and I can't find anybody else who has done anything similar to what I have in mind. Its getting frustrating as this was going to be a little christmas present for my sister and time is ticking. My lack of experience as a sewer is really showing on this little project. Tomorrow I might try doing it using bias binding instead.