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Preheat the oven to 350° and line a baking sheet with parchment paper or foil.
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Using a 2-inch round biscuit cutter, cut the potato slices into rounds.
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In a bowl, toss the potatoes with the olive oil and arrange them in a single layer on the baking sheet.
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Season lightly with salt and pepper, then sprinkle with the cheese.
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Bake the potato rounds for about 45 minutes, or until deep golden; let cool. Transfer the potato coins to paper towels.
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In a small bowl, combine the ham with the mayonnaise, scallion, Cornichons, capers, tarragon and mustard.
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Season with salt and pepper.
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Spoon the ham salad onto the potato coins and serve.