You will also need a baking dish measuring approximately 20x24cm, lightly buttered. Pre-heat the oven to 200°C/Fan 180°C/Gas 6.
Cut the bread into 1cm thick slices, leaving the crusts on. Toast on a low setting, until lightly crisp. Spread the toast generously with the butter. Cut the Comté into 1cm thick slices. Tear the ham into large bite-sized pieces. Pull the thyme leaves from their stems.
Place a single layer of the buttered bread on the bottom of the dish, tucking the slices together snugly. Place some of the cheese slices and ham on top, add a little black pepper, some thyme leaves then another layer of buttered bread and more of the cheese slices and ham. Continue until the ingredients are used up finishing with a bread layer.
In a mixing bowl, add 50g grated Parmesan, egg yolks, nutmeg then mix in the double cream and milk with a fork or small whisk. Season with a little salt then pour over the bread letting it trickle down through the layers. Grate the remaining 50g Parmesan over the surface.
Cover the top of the dish with foil and bake for 35 minutes. Remove the foil and continue baking for a further 10 minutes until the top is golden. Remove from the oven and leave to settle for 10 minutes before serving.