Set up your Big Green Egg for an indirect cook with the stainless steel grid on top of your ConvEGGtor. Set your Egg to 200°C.
Cut your leeks into 2cm rounds and pop into the bottom of an ovenproof baking dish. We don't cook our leeks but if you wanted to shorten the cooking time you could steam for 6 to 8 minutes until the leeks are tender.
To make the sauce, you start with a classic roux, so melt the butter in a pan and then stir in the flour. Keep stirring, you're looking to make a thick paste. Once you've got a paste, give it a couple of minutes to cook the flour; you'll start to see bubbles forming in the paste.
Add the milk gradually, a bit at a time, stirring continously, until all the milk has been added. As the milk heats up, it will start to thicken, so keep stirring to avoid any lumps forming.
You're looking for the sauce to coat the back of a spoon, at this point you can stir in the dijon mustard.
Remove from the heat and add the cheese. The cheese will melt in the residual heat of the sauce. If you plan to add breadcrumbs, then keep back a little cheese to mix through the breadcrumbs.
Taste the sauce; we season with a little salt and lots of ground black pepper. We might even add a bit more mustard and or cheese depending how the sauce tastes.
Now you can pour the cheese sauce into the dish to cover the leeks. If you're making the gratin, you can add the breadcrumb topping at this stage.
Place the dish on the grid and cook for about 40 minutes until the top is crisp and bubbling and the leeks have softened.
Once cooked, remove from the heat and serve with your favourite roast or preferred dinner.