Preheat the oven to 200 degrees C. Lightly grease a large baking dish or four individual ovenproof dishes with melted butter.
Cook the potatoes and carrots in a large saucepan of lightly salted boiling water for 10 minutes. Reduce to a simmer, add the beans to the pan and cook gently for a further 5 minutes.
Meanwhile, rub the butter into the flour, either in a bowl using your fingertips or in a food processor. Stir the cheese into the crumbly flour mixture.
Drain the vegetables and toss them with the garlic, parsley and pepper to season. Tip into the prepared dish or dishes. Pour over the cream, then cover with the cheese crumble. Bake for 30 minutes (20 minutes for individual dishes) until golden and crispy. Serve immediately.