Preparation Place porcini in medium bowl. Pour 1 cup hot water over. Cover; let stand until softened, about 30 minutes. Using slotted spoon, transfer porcini to work surface. Chop porcini. Pour soaking liquid through strainer lined with wet paper towel and set over small bowl; reserve liquid. Heat oil in heavy large skillet over medium-high heat. Add shiitake mushrooms; sauté until tender and beginning to brown, about 6 minutes. Add shallots; sauté 2 minutes. Add porcini. Pour in reserved soaking liquid. Boil until almost all liquid evaporates, about 2 minutes. Season with salt and pepper. Transfer to bowl. Cook broccoli in pot of boiling salted water until just tender, about 2 minutes. Drain. Transfer to bowl of ice water; cool. Drain. (Mushrooms and broccoli can be made 1 day ahead. Cover separately; chill.) Melt butter in large skillet over medium-high heat. Add mushrooms and broccoli; sauté until heated through, about 5 minutes. Season with salt and pepper.
Preparation Place porcini in medium bowl. Pour 1 cup hot water over. Cover; let stand until softened, about 30 minutes. Using slotted spoon, transfer porcini to work surface. Chop porcini. Pour soaking liquid through strainer lined with wet paper towel and set over small bowl; reserve liquid. Heat oil in heavy large skillet over medium-high heat. Add shiitake mushrooms; sauté until tender and beginning to brown, about 6 minutes. Add shallots; sauté 2 minutes. Add porcini. Pour in reserved soaking liquid. Boil until almost all liquid evaporates, about 2 minutes. Season with salt and pepper. Transfer to bowl. Cook broccoli in pot of boiling salted water until just tender, about 2 minutes. Drain. Transfer to bowl of ice water; cool. Drain. (Mushrooms and broccoli can be made 1 day ahead. Cover separately; chill.) Melt butter in large skillet over medium-high heat. Add mushrooms and broccoli; sauté until heated through, about 5 minutes. Season with salt and pepper.