Preheat the oven to 450°F. Wash and dry the fresh produce. In a bowl, combine the dried porcini mushrooms and 1 1/2 cups of hot water; let stand for at least 10 minutes. Cut the broccoli into small florets. Peel and small dice the carrots. Small dice the celery. Roughly chop the oyster mushrooms. Cut off and discard the root ends of the scallions; thinly slice, separating the white bottoms and green tops. Pick the thyme leaves off the stems; discard the stems and roughly chop the leaves. Grate the cheese.
Line a sheet pan with aluminum foil. Place the broccoli on the prepared sheet pan. Drizzle with olive oil and season with salt and pepper. Toss to thoroughly coat. Arrange in a single, even layer. Roast 12 to 14 minutes, or until lightly browned and tender when pierced with a fork. Remove from the oven, leaving the oven on. Carefully transfer to a plate and set aside in a warm place. Discard the foil.
While the broccoli roasts, reserving the water, carefully transfer the porcini mushrooms to a cutting board; roughly chop. In a large, high-sided pan (or pot), heat 2 teaspoons of olive oil on medium-high until hot. Add the carrots, celery, oyster mushrooms, chopped porcini mushrooms, thyme and white bottoms of the scallions. Season with salt and pepper. Cook, stirring occasionally, 12 to 14 minutes, or until softened.
Add the butter to the pan and cook, stirring frequently, 30 seconds to 1 minute, or until melted. Add the flour and cook, stirring frequently, 30 seconds to 1 minute, or until lightly browned. Slowly stir in the reserved mushroom water. Cook, stirring occasionally, 2 to 4 minutes, or until the mixture is slightly thickened. Add the roasted broccoli and stir to combine. Turn off the heat and season with salt and pepper to taste.
Transfer the finished filling to a baking dish. Bake 8 to 10 minutes, or until thickened and bubbling around the edges. Remove from the oven. Let stand for at least 2 minutes before serving.
While the casserole bakes, lightly oil the sheet pan used to roast the broccoli. Place the pastry rounds on the prepared sheet pan in a single layer. Evenly top with the cheese; season with salt and pepper. Bake 8 to 10 minutes, or until lightly browned and puffed up. Remove from the oven. Divide the baked casserole and baked pastry rounds between 2 dishes. Garnish with the green tops of the scallions. Enjoy!