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1
Combine the flour and salt in a bowl. Make a well, add the eggs, and whisk inward, gradually drawing in the flour. Add the milk in a slow stream, whisking until the batter is smooth and free of lumps. Stir in the melted butter. The batter should coat a spoon in a thin, even film. Rest for at least 30 minutes — or refrigerate overnight.
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2
Melt the butter in a wide frying pan over medium-high heat. Add the shallots and sweat until softened. Add the finely chopped mushrooms, raise the heat, and cook, stirring frequently, until all moisture has evaporated and the duxelles is completely dry. This is where the dish lives or dies: press the duxelles with the back of a spoon — no liquid must seep out. A wet duxelles will make the crêpes soggy beyond rescue.
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3
Remove the duxelles from the heat. Fold in the 150 ml crème fraîche and the diced ham. Stir to combine. The mixture should be cohesive and spreadable, not loose.
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4
Cook the crêpes in a lightly buttered pan over medium-high heat: pour a small ladleful of batter, tilt the pan to spread it as thin as possible, and cook until the edges lift and the underside is pale gold. Turn once briefly. Stack on a plate. The crêpes must be thin — thick crêpes will turn doughy under the gratin.
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5
Butter a gratin dish. Lay a crêpe flat, spread 2 to 3 tablespoons of the mushroom-ham filling across the centre, and roll it into a tight cylinder. Place seam-side down in the dish. Repeat with the remaining crêpes, arranging them closely packed in a single layer.
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6
Pour the 200 ml crème fraîche generously and evenly over the ficelles. Scatter the grated Gruyère or Emmental over the surface in an even, thick layer. Heat the oven to 200 °C.
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7
Bake for 15 to 20 minutes. The dish is ready when the cream is visibly bubbling at the edges and the cheese has formed a deep golden-brown crust across the surface. A pale or merely melted cheese indicates the gratin is underdone.