Preheat the oven to 425 degrees and use a butter knife to scrape the gills out of the mushroom caps. In a small bowl, whisk together the oil, marsala wine, garlic, thyme, salt, and pepper. Brush the outside and inside of the mushroom caps with the mixture, then arrange in a single layer, cap side-down, on a lightly greased baking sheet. Roast about 8-10 minutes. If the mushrooms give off a lot of liquid, blot it up with a paper towel.
Meanwhile, heat the remaining tablespoon of olive oil in a skillet over medium heat. Add the shallots and mushrooms and cook, stirring often, until the mushrooms are browned and softened, 6-8 minutes. Stir in the chicken, marsala wine, tomato paste, and thyme, and cook, stirring frequently, until the wine has evaporated. Taste and season with salt and pepper. Rremove from heat and stir in the mascarpone cheese, 1/4 cup of the Gruyere cheese, and the panko bread crumbs. Stir until the cheese has melted.
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