Trim, wash and slice the leeks on an angle, about 2cm thick. Peel and slice the garlic.
Put a large casserole-type pan (ideally one you’d be happy to serve in) on a medium heat and add a drizzle of oil, the butter, thyme leaves and garlic.
As things begin to bubble and fry, stir in the leeks. Leave to cook, and check on it every few minutes to stir and make sure it doesn’t catch.
At this point, you have two choices: one is good, one is great. You can either stir the rest of the ingredients into the leeks, grating in the Cheddar and Parmesan, and tearing in the brie. Put it into the oven to cook for 45 minutes uncovered, or, if you want the sweetest leeks in the world (and I think you do), do the following...
Turn the heat under the pan down a little and cook the leeks for about 35 minutes, or until soft and intensely gorgeous, stirring every now and then.
Season, then spoon it all into a dish, or leave in the pan.
Stir in the cream and splash of water, grate over the Cheddar and Parmesan, then pull the brie into parts and bomb those on top.
Pop in the oven for 15 minutes, or until golden and bubbling.