Peel the parsnips and carrots. Cut them into ¼ inch thick pieces.
Put the parsnips, carrots, water, and oil in a medium-sized skillet. Heat on medium with the lid on for 10 minutes.
Meanwhile, cut the zucchini into quarters lengthwise and then into ½ inch thick pieces.
After the parsnips and carrots have been cooking for 10 minutes, add the zucchini, peas, parsley and salt to the skillet. No lid this time. Cook for approximately 30 more minutes, stirring every 10 minutes.
Remove from heat when the zucchini is the desired softness.