1 sheet puff pastry (from a 17.3 oz package), defrosted
3 tbsp. unsalted butter, divided
1 large shallot, minced
1 tsp. minced fresh thyme leaves
1 lb. mushrooms (preferably a mix of cremini and wild), stems removed and sliced 1/4-inch thick
Freshly ground black pepper
1/2 tsp. white truffle oil, plus more for drizzling
3 tbsp. dry white wine
1 1/4 c. baby arugula, divided
8 oz. fresh burrata, carefully sliced into 1/2-inch rounds
1 egg, beaten with 1 tbsp. water, for egg wash
Crushed red pepper flakes, for serving (optional)
Preheat oven to 400 degrees F.
On a floured surface, unfold the sheet of puff pastry and roll it into a 12-inch square. Using a mixing bowl, or other circular object as a guide, cut an 11-inch circle from the sheet of puff pastry, discarding the scraps. Carefully transfer the pastry to a sheet pan. Using a sharp knife, score a 3/4-inch border around the circumference of the pastry. With a fork, prick dough inside the border, approximately every ½-inch. Refrigerate until ready to use.
Meanwhile, in a large sauté pan, heat 2 tablespoons of the butter over medium heat. When the butter is hot, add the shallots and thyme and cook for 3 to 5 minutes, stirring occasionally, until the shallots are translucent. Add half the mushrooms, cover and turn the heat down to medium low. Cook for 5 to 7 minutes, until the mushrooms are cooked through and significantly decreased in size.
Add the remaining mushrooms, 1 ½ teaspoon salt, 1 teaspoon pepper, the remaining tablespoon of butter and the ½ teaspoon truffle oil. Raise the heat to medium and cook uncovered, stirring occasionally, until the second batch of mushrooms are just cooked through, but not reduced in size, about 5 minutes. Add the wine and cook for one more minute, until all the liquid has evaporated.
Off the heat, add ¾ cup arugula and toss.
Set the mushrooms aside and bake the prepared pastry circle for 10 minutes, until just barely tender. Using a spatula, carefully spread the mushrooms over the top of the pastry so they evenly cover the surface within the scored border.
Artfully arrange the burrata on top of the mushroom and sprinkle with salt and pepper. Using a pastry brush, gently brush the scored crust with the egg wash. Bake the tart for an additional 10 minutes, until the burrata is just heated through.
Sprinkle the tart with the remaining ½ cup of arugula, drizzle with truffle oil, and sprinkle with red pepper flakes, if using.
Serve immediately, or reheat in a low oven before serving.