Preheat the oven to 400 degrees F. Line a baking with parchment.
Combine the parsley, thyme, 1/2 teaspoon salt and a few grinds of pepper in to a food processor and process until finely chopped. Add the butter and process until well combined and the butter is very green. Clean out the food processor.
Carefully remove the leaves and any small inner leave from the bottom of the cauliflower and trim the stem so it is 1/2-inch-long. Brush the cauliflower with 2 tablespoons of the herb butter and sprinkle with 1/2 teaspoon salt and a few grinds of pepper. Transfer to the prepared baking sheet and bake until a paring knife can easily be inserted and removed from stalk and the cauliflower has turned a light golden brown, 25 to 30 minutes.
Meanwhile, pulse the mushrooms in a food processor until a paste. Melt 2 tablespoons of the herb butter in a large nonstick skillet over medium-high heat. Add the mushroom paste, 1 teaspoon salt and a few grinds of pepper and cook, stirring occasionally, until all the moisture has evaporated, about 10 minutes. Let cool slightly, about 10 minutes.
Place 1 puff pastry sheet on top of the other. Roll out to a 14-by-14-inch square with a 3-inch-wide border all the way around that is considerably thinner than the middle. Round the corners so you have a 13-inch circle. Brush the puff pastry with the Dijon, then spread the mushroom mixture over top. Turn the cauliflower upside down on top of and in the middle of the puff pastry circle. Melt the remaining herb butter in the microwave in 30 second intervals. Pour the butter in between the stalks of the florets. Fold the puff pastry around the cauliflower so that the whole thing is enclosed. Turn the cauliflower right side up, place it back onto the prepared baking sheet and brush with the egg. Sprinkle with 1/2 teaspoon salt and bake until the puff pastry is a deep golden brown and a paring knife can be easily inserted, twisted and removed from the stem of the cauliflower, 55 to 60 minutes. Let cool for 10 minutes before serving. Slice through the middle then into wedges.
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