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Preheat the oven to 180ºC/350ºF/Gas Mark 4.
Begin by making a roux. Melt the butter in a pan and whisk in the flour - it should become a crumbly mixture. Continue to gently whisk while slowly adding the warmed milk, until a paste has formed which is the consistency of double cream. You may not need to use all the warmed milk.
Add the cheese, anchovy paste and salt and pepper. Whisk all together until the cheese has melted. Take off the heat for 5 minutes.
When cool enough to touch, add the egg yolks and a teaspoon of warm water, then whisk together.
Prepare four ramekins, or a large dish, by rubbing the edges with butter, then chilling them in the fridge.
In a separate bowl, whisk the egg whites until peaks form and hold stiff peaks.
Fold ¼ of the egg whites into the mixture and mix thoroughly - this will bind the egg whites and the mixture together. Then very gently using a wooden spoon, fold the remaining egg whites into the mixture, taking care to keep as much air in the mixture as possible.
Pour the mixture into the ramekins up to approximately ⅔ deep.
Place ramekins on a preheated baking tray and using a blow torch, quickly and lightly, brown the tops before placing in the oven for 10-12 minutes. Serve immediately.