Strain the porcini mushrooms in a fine-mesh sieve and reserve the soaking liquid. Chop the mushrooms and set aside.

Heat 2 tablespoons butter with the olive oil in a large Dutch oven or sauce pan until foamy. Add the arborio rice and cook, stirring frequently, until the rice is well coated and fragrant, 1 to 2 minutes. Add 1 1/2 tablespoons shallots and 1/2 tablespoon garlic and cook, stirring, until fragrant, about 1 minute. Add the reserved porcini soaking liquid and cook until it evaporates. Reduce the heat to medium and add 2 cups chicken stock and 3/4 teaspoon salt. Cook, stirring constantly, until the broth has been absorbed. Continue to cook, adding more broth, 1/2 cup at a time, until it is absorbed and the rice is al dente, 16 to 18 minutes total cooking time. (You may not need all 6 cups of the broth.) Add the thyme, rosemary, and 1/4 teaspoon black pepper. Set aside while you prepare the mushrooms.

Heat the remaining 2 tablespoons butter in a large skillet until foamy, 1 to 2 minutes. Add the remaining 1 1/2 tablespoons shallots and the remaining 1/2 tablespoon garlic and cook until fragrant, about 1 minute. Add the white button mushrooms, 1/2 teaspoon salt and 1/4 teaspoon black pepper and cook, stirring frequently, until the mushrooms release their liquid, about 4 minutes. Add the reserved porcini mushrooms and continue to cook, stirring, for 6 minutes, or until all the liquid evaporates and the mushrooms are golden brown around the edges. Add the soy sauce and parsley and cook for 1 minute. Add the white wine and cook until evaporated, 2 minutes. Remove from the heat.

Layer half of the reserved risotto in a 9 by 9-inch casserole or baking dish and sprinkle with half of the Parmesan. Top with the mushroom mixture. Add the remaining risotto and top with the remaining Parmesan.

Preheat the oven to 350 degrees F.

In a small bowl, whisk together the eggs, cream, and the remaining 1/4 teaspoon salt and pinch of black pepper. Pour the mixture evenly over the top of the casserole and bake, uncovered, for 30 minutes or until golden brown. Remove from the oven and let stand for 5 minutes before serving.