If you have a path you created with the Pen tool, select the Brush and press Enter to stroke the path with the Brush.(or any painting tool - Eraser, Smudge, etc.). You can also do this via the Paths panel menu, and the hollow circle icon at the bottom of the paths panel will stroke with the last-used tool.
She just used the Brush tool to loosely trace the leaf. You can do the same thing in Photoshop with the Brush tool. Be sure to create and name new layers for the leaf, the tracing, and the blobs. Hide the leaf layer when finished.
Youu can't really make a one pixel line with the brush because even a one pixel preset has some anti alias. What you can use is the pencil. The two lines below are zoomed in to 400%. The upper line is one pixel fully hard black brush preset, and the lower line the same thing using the pencil. ipso facto, I rest my case 😉
If the Pen tool is the problem, you have two options in Photoshop for doing this without the Pen tool.
You could use the Brush tool. But the problem is that in Photoshop, the Brush tool is pixels only, so if you need to edit the stroke, you have to erase and re-paint some pixels, which might make it look less natural.
You could use the Freeform Pen tool (see demo below). This might be a better solution, because it takes care of both problems. First, unlike the Pen tool, you drag the Freeform Pen tool normally like a brush, so it does not depend on being comfortable with the Pen tool. Second, it creates a vector shape layer instead of pixels, so you can quckly edit the resulting path as you would in Illustrator. To create a one line drawing with the Freeform Pen tool, make sure Fill is set to None.