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Preheat oven to 400 degrees. Line a cookie sheet with parchment paper.
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Lay out the puff pastry sheet, poke with a fork a few times, and baste with egg yolk.
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Par-bake the puff pastry for 5 minutes.
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In a medium sized frying pan set on medium high heat, melt the butter. Add shallots and mushrooms and fry until the mushrooms have released the excess water (about 5 minutes). Drain and set aside.
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To make the béchamel sauce, sauté garlic in a pan with the butter, until soft (about 3 minutes), on medium heat.
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Add flour, salt and pepper, and thyme leaves, and whisk together until flour has absorbed the butter.
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Slowly add the half and half until while continuously whisking, until mixture has thickened and will coat the back of a spoon.
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Once done remove from heat.
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Spread béchamel sauce over puff pastry. Spoon chanterelles and shallots over the béchamel sauce and sprinkle with fresh arugula and Gruyère cheese.
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Bake tart for an additional 15 minutes or until the edges of the pastry is golden and puffy and the cheese has melted.
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Serve warm or room temperature.