I've gone over the outline in micro-pigment pen. Sometimes I went a bit wonky, because of the lumps in the linen and not gone quite where I wanted to go, but it's all fixable as I go alone and outline in thread.

I've done one stem, and 3/4 of another in 3 shades of brown/green neutrals, in chain stitch. 7 stitches wide. The 'cut' bases of the stems are done in satin stitch. The chain stitch takes forever but I do like it.

On my first attempt, on the shorter stem, I did the outline in the green used to outline the leaves above, as it said to in the book, but I didn't like the effect. (remembering that I've changed the colours to ones I wanted to use - it would have worked better with the olive green Trish suggested).

Chain stitch is a bugger to rip out, and I slipped with my ripper and took out a bit of the linen.
In the enlargement of the picture it might be visible. It's to the right of the stem near the bottom.

I 'Fray-Check'ed the area, let it dry and then 'Fray-Check'ed it again. That meant that the area I had to re-sew was stiff and sewable upon, and the area to the side wouldn't unravel anymore.

Edit :

Here's a photo I took of the embroidery, rather than using the scanner. It's a bit clearer and brighter.