Place a saucepan over a low heat and melt the butter.
Add the chopped leeks and gently sweat for 10-15 minutes, stirring occasionally, until very soft and sweet but not browned.
Stir in the flour to coat the leeks and cook for 1 minute, stirring constantly.
Gradually whisk in the milk, a little at a time, to create a smooth, thick sauce.
Bring to a simmer and cook for 1 minute.
Remove the pan from the heat and let it cool for a few minutes. This is crucial to prevent the eggs from scrambling.
Fold in the grated Cheddar until it has melted, then stir in the egg yolks.
Season generously with sea salt and freshly ground black pepper.
Preheat your grill (broiler) to a medium-high heat. Lightly toast the slices of bread on one side only.
Turn the bread over to the untoasted side and spread the leek and cheese sauce generously all the way to the edges.
Place the rarebits under the grill and cook for 3-5 minutes, or until the topping is golden, bubbling, and cooked through.
Serve immediately, with a drizzle of brown sauce if desired.
Add a teaspoon of Dijon mustard or a splash of vegetarian Worcestershire sauce to the cheese mixture for an extra tangy flavour dimension.