Preheat the oven to 400°F. Cook the potatoes in a pot of salted, boiling water for 15-20 mins until tender.
Heat the oil in a deep frying pan, add the onion, carrot and mushrooms and sauté for 3-4 mins, stirring. Season and mix in the thyme. Stir in the tomato paste, leeks, garlic, wine and stock. Bring to a boil and simmer for 1-2 mins.
Mix the cornstarch into the vegetables and continue to stir until the sauce thickens. Season with salt and pepper.
Drain the potatoes and add the milk, butter, sour cream and nutmeg. Mash until smooth and season. Grease a baking dish with butter then transfer the potatoes to the dish. Spoon the vegetable mixture into the center then crumble the feta on top. Bake for 25-30 mins until golden and bubbling. Serve.