adobe illustrator - How to overlap a continuous line on itself?

Yesterday I tried to create the following shape:

Following the path from the top it goes round, crosses over itself (bottom left), goes around again and passes under itself before going back up again. The paper sketch was easy to make.

However, in Illustrator I expected to create this with a single path and an outline of that path. With a single path I ran into the problem that it could never pass over itself. The boundaries would then disappear:

Then I went ahead and made it in a convoluted way with multiple elements, which made editing very slow and rigid:

Now I am wondering how I can recreate this image (or any self-crossing path) using a more flexible method which allows for easy editing afterwards.

Answer

It is possible to do this without cutting the curve. What you do is you use the appearance panel to overlay 2 strokes on top of each other. Then over this layer copy the same strokes, but this time with a dash that is set up so that the stroke only covers a part of the curve.

Image 1: A path that overlaps itself.

This works irrespectivelly wether the curve is open or closed. There is also a an alernative approach for this problem that has been answered before in the question: