The quirkiness continues in the "flowers" -- both big round spheres that are worked in spiral trellis stitch using two colors in the needle so the result is sort of tweed-like.
Thistle-Threads has excellent instructions for this stitch here. The first photo below shows the completed green and yellow flower and the backstitched outline for the larger flower. The backstitch provides a scaffolding for the stitch.
Here are two photos of the stitch being worked. First, the needle is inserted from the center of the shape outwards, then the working thread is looped counter-clockwise around the needle. Pulled tight, this creates a series of knots that creates the stitch pattern.
In the photo, it looks like I'm going from the outside towards the inside, but I'm not. Usually you'd use a tapestry needle with a blunt point for this stitch. But I find that towards the center, I often need a sharp point to help find the little tiny spaces. So I use an embroidery sharp, and just stitch "eye first" when I need a blunt point. That's what's happening here.
For me, the tricky part of this stitch is getting the little knots to sit close to the previous row instead of floating all over the place. What works for me it placing the needle into the loose knot, then pulling the knot tight as the needle holds it where it belongs next to the previous row.
Here's the completed monster flower motif. (It's almost as big as the woman who stands just to the right.) The photo below shows a close up of the stitch. I think you can see some of the spiral pattern, but the tweeding of the two colors does minimize the spiral look.