Trim, wash and finely slice the leeks. Peel and finely slice the garlic and pick the thyme leaves, then place in a large casserole pan on a medium heat with the butter and 1 tablespoon of oil. Once sizzling, stir in the leeks and 400ml of water, then cover and simmer gently over a low heat for 40 minutes, or until sweet and soft, stirring occasionally. Season with sea salt and black pepper. When the leeks are almost done, cook the pasta in a large pan of boiling salted water according to the packet instructions, then drain, reserving a mugful of starchy cooking water. Toss the drained pasta into the leek pan, then remove from the heat and wait 2 minutes for the pan to cool slightly while you finely grate the cheese and beat it with the egg (if the pan’s too hot, it’ll scramble; get it right and it’ll be smooth, silky and deliciously elegant). Loosen the egg mixture with a splash of reserved cooking water, then pour over the pasta, tossing vigorously (the egg will cook in the residual heat). Season to absolute perfection, going a little OTT on the pepper. Adjust the consistency with extra cooking water, if needed, and finish with a little stroke of cheese. Fantastic served with a glass of cold Italian white wine.