I started on a "scribble lace" shawl, which, being knit on 10mm balloons, didn't take long to finish:
[scribble lace shawl]
The "scribble" is a single row ("back" and no "forth") of bulky yarn, and the background is lace-weight yarn (in this case, a silk/mohair blend). You use double-points or a circular needle so that you can shove the work to the end of the needle where your working yarn is; this changes periodically because of the single thick row. It takes about 100m of thick yarn and 4x that in thin to make a 32"x70" stole, if you have (on average) 4 rows of thin yarn to every 1 row of thick. For this project I increased and decreased the number of rows of thin yarn from 3-5 (sometimes even 6) and back again to give the stripes a subtle "motion".
I love this idea. It is a fantastic way to showcase those homespun art-yarns that I love but, until now, had no idea what to do with! You can use ribbon, too.
The one thing that is useful to know when making these shawls is how to match the cast-on and bind-off. They both need to be quite elastic because the fabric is so stretchy. Start and end with the thick yarn to give a stable edge to the shawl.
I used a "knit-on cast-on", and my bind-off, which matches very closely, is variously referred to as a "knit bind off", a "lace knit bind off", or a "russian bind off". Here's a write-up. It's pretty easy. I use it all the time for toe-up socks. For me, this bind-off falls between the YoBo (yarn-over bind-off or JSBO) - which I find very loose - and the standard knit-one-pass-over bind off (which is too tight for toe-up socks).