4: In a large saucepan over high heat, pour in 4 tablespoons olive oil and when hot, add onion, salt and pepper. Cook for 1 minute, without browning.
5: Add the carrots and leeks, mix well, season with salt and pepper and cook, uncovered, until the carrots are tender (about 5 minutes). Transfer to a large plate.
6: In the same saucepan, still over high heat, pour in 4 tablespoons olive oil and when it's hot add 1 bayleaf, 1 sprig thyme and 1 garlic clove. Stir to flavour the oil, then add 500 g minced beef, salt and pepper. Cook the meat to your liking, stirring occasionally.
7: Add 250 g peeled and chopped tomatoes, mix well, bring to the boil, then turn off the heat and remove (and discard) the bay leaf, garlic and thyme.
11: Spread the polenta in the dish, leaving a tiny space around the edge for the cooking steam to escape, then sprinkle the top with the remaining grated cheese.
12: Bake for about 30 minutes at 200°C (390°F), watching for browning on top.
13: Your polenta parmentier is ready.
Remarks
For the grated cheese, it's up to you, but I'd recommend a hard cheese: Comté, Cheddar, Parmesan... The proportions are only indicative, so don't hesitate to adapt them to your taste and the quantities you have on hand.