Preheat the oven to 375 degrees F. Line a sheet pan with parchment.
Put the olive oil and butter in a large skillet over medium-high heat. When the butter has melted and the oil is hot, add the onion, minced rosemary, thyme and garlic and stir to combine. Add the mushrooms and cook until golden, about 5 minutes. Season with a good pinch of salt and pepper, then stir. Deglaze the pan with the wine and continue to cook until the wine has reduced, about 1 minute. Set aside.
In a small bowl, make an egg wash by beating the egg with 1 tablespoon of cold water.
Lay out the puff pastry sheet on a floured surface and pile the mushrooms in the middle. Place the wheel of Brie in the center. Fold up the sides of the puff pastry to enclose the mushrooms and Brie, folding in the edges to seal. Place the wrapped Brie on the prepared sheet pan seam-side down and brush with the egg wash.
Bake until golden, 30 to 35 minutes. Allow to cool slightly, then top with rosemary sprigs and dried cranberries to resemble an evergreen bush with berries.