Cut any coarse part off the bottom of the asparagus and put aside. Clean the potatoes and boil in salted water with the ends of the asparagus – they should only take about 10 minutes.
Meanwhile have the asparagus tips tied in a bundle and steam. This should take about 5–10 minutes depending on the thickness of the stems.
When both vegetables are cooked, remove the coarse asparagus stems from the potatoes and put the potatoes on a warmed serving dish, surrounded by the asparagus tips. Pour over the melted butter with a little lemon juice added and sprinkle with a little chopped parsley.