In a small container, combine vegetable broth with cornstarch. Carefully add to meat mixture, stirring until it starts to thicken. Add extra broth if needed. Stir in chopped zucchini & cover. Turn heat to low & cook gently while preparing the parsnip topping.
Turn oven on to broil. When parsnips are soft, mash thoroughly. Stir in butter, milk & grated cheese. Spoon pork mixture into an ovenproof dish. Evenly spread the cheesy parsnip mixture on top. Place under a broiler until the topping starts to brown. Serve immediately.