I'd imagine its really a combination that would create something like that. Lets for example say

from the site above - this is not my work.
There is roughly three main planes in this work. The blue background, the black middle ground and the white foreground.
Foreground Black Part
If you started with the foreground black, these seem to be a mixture of vector shapes, images and buildings (so this could either be photoshop's threshold tool or illy's image trace tool) added with illy drawn parts and hand pieces. You effectively have a church above and a jesus statue below, coupled with some curve lines that (a drawn line with a rounded cap end in illy will make these)
Blue Background
This is mostly texture to enhance the effect of the black, Its circles and lines (try creating circles of differing sizes and stroke weights then aligning them).
White foreground
Part of this layer is to remove whats gone before, because its the same colour as the canvas, This effect can work very well on type also. Make an vector/image white and place over selectively. The other part to the left is a more typical drawn element. It may have been traced and then draw in illy. To create something as good as that simple takes time and skill. It often helps to think of items as parts - so maybe try the trunk first (duplicate and you have two) then the ear and build it up.
Final words
This is only my interpretation of how you might go about creating something like this. Its not supposed to be the end word in it and I don't claim to say it will work. Simply I am offering a starting point from what I can understand of the image. I've not created the work above. I've taken it from the site and explained how one could create it.
This is not my work, only my tutorial how it might be done. sorry for any confusion caused.