Preheat the oven to 400 degrees F. Line a baking sheet with parchment paper.
Melt the butter in a small skillet over medium heat. Add the walnuts and cook, tossing occasionally, until lightly toasted, 1 to 2 minutes. Add the thyme, season lightly with salt and toss. Stir in the brandy and remove from the heat. Transfer to a small bowl and stir in the dried apricots and preserves. Let cool to room temperature.
Place the Brie on the center of the prepared baking sheet and cut off the rind on top. Spread the apricot compote evenly over the top of the Brie.
Unroll the puff pastry sheets on a floured work surface. Brush a 2-inch strip down the long edge of one sheet with the egg and line up the second sheet with the first, overlapping the edge brushed with egg so that the two stick together. Flour the pastry well and roll with a floured rolling pin to make a 14-inch square. Trim the corners from the pastry to make a circle (you want to make the largest circle possible). Reserve the trimmings. Transfer the pastry to the baking sheet and cover the Brie. Tuck the edges underneath the Brie.
Reroll the pastry scraps and cut out five or six 2-inch leaf shapes, then score them with the back of a butter knife to create simple veins in the leaf. Brush the pastry-wrapped Brie with the egg. Arrange the leaves decoratively on top of the Brie and brush with the egg.
Bake the brie until the pastry is puffed and deep golden, about 40 minutes. Let stand about 20 minutes before serving with apple and pear slices and crackers.
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