For the puff pastry: Preheat the oven to 400 degrees F. Line a baking sheet with parchment.
Using a 4-inch ring mold, cut out 4 circles of puff pastry. In a small bowl, whisk together the egg and a splash of water. Brush the top of each pastry round with the egg wash and place on the lined baking sheet. Bake until the rounds puff up and the tops are light golden, about 15 minutes. Remove and set aside. Lower the oven temperature to 375 degrees F.
For the beef: In a large pan over medium heat, add the butter, olive oil and beef, broken up in small chunks. Sprinkle over 1 tablespoon salt and a few grinds of pepper and cook, stirring, until browned, about 5 minutes. Transfer the beef to a 9-by-13-inch baking dish using a slotted spoon. Pour the pan juices into a bowl and reserve.
For the mushrooms: In the same pan, add the butter and olive oil and heat over medium heat until the butter melts. Add the mushrooms and cook until they release their liquid, wilt and gain a bit of color, 8 to 10 minutes. Add the garlic, thyme and onion and season with salt and pepper. Cook until fragrant, about 4 more minutes. Add the mushrooms to the baking dish on top of the beef layer.
For the sauce: Combine the butter and flour in a microwave-safe mug and microwave on high for 1 minute and 30 seconds.
In a pan over medium heat, add the mustard, flour-butter mixture and reserved beef drippings and whisk together. Add the stock, plenty of black pepper and a pinch of salt. Bring to a simmer; simmer until the sauce thickens, 5 to 8 minutes. Remove from the heat and stir in the parsley.
Pour the sauce on top of the dish, over the mushrooms and beef. Place the pastry rounds on top. Bake, uncovered, until the dish bubbles, 15 to 20 minutes.