A classic bearnaise sauce is made from eggyolk, clarified butter, vinegar, tarragon, shallots and pepper. I experimented a bit and came up with this vegan sauce which kind of looks like bearnaise and has the same seasoning.
Parsnip bearnaise sauce Sautee some shallots for a few minutes with white pepper and tarragon. Add some white wine vinegar and then some peeled chopped up parsnips (and some root celery if you like) and water to cover. Also put some good vegetable stock. Cook until soft and blend smooth. Add coconut milk, a little tumeric (just for color), more tarragon and some sea salt. Taste to see if it needs more vinegar. Heat up gently and there you have it- Parsnip bearnaise.