1. In a small bowl, pour 1 1/4 cups boiling water over porcini. Let sit 30 minutes.
2. Preheat oven to 425°. With a slotted spoon, transfer porcini to a cutting board, reserving mushroom liquid. Finely chop porcini and set aside.
3. In a medium saucepan over medium heat, melt butter in 1 cup reserved porcini-soaking liquid (if you don't have enough liquid, add water to make 1 cup). Bring to a boil, reduce heat to low, and dump in flour. Stir vigorously until mixture forms a ball that pulls away from sides of pan, about 1 minute. Remove pan from heat.
4. Stir in eggs, 1 at a time. Dough will separate after each addition; stir until it forms a smooth paste before adding next egg. Stir in porcini, parmesan, 1/2 tsp. salt, and 1/4 tsp. pepper.
5. Butter 2 baking sheets. Drop mixture by heaping tablespoonfuls 1 in. apart onto sheets. Sprinkle lightly with additional salt and pepper. Bake until puffed and brown, about 30 minutes. Cut slits in sides of puffs, turn off oven, and return puffs to oven for 10 minutes. Serve warm.
Note: Nutritional analysis is per puff.