Hi Thor - in a future version I would like to make a tool that would surface a curve like that directly, but MoI won't have that for version 1.0 .

In general the best way to surface a closed thing like this right now is to dice it up into at least 2 pieces and then do something with those pieces, either loft between them, or use them as rails for a sweep, or part of a network surface.

So what I'd recommend is to first draw a line down the middle like this:



Now select your outline, then run Edit/Trim and select the line as the cutting object. Hit done to keep all pieces.

Now your outline should be split into 2 different pieces. In this case I think a loft between these will get you a good result, select both of the pieces and hit Construct / Loft and push done, to get this:



Sometimes it is easier to make progress by splitting things up like this.

Hope this helps!

- Michael