- Preheat oven to 375°F.
- Spread walnuts on baking sheet, and toast in oven until lightly browned and fragrant, about 6 minutes. Set aside to cool.
- Reduce oven temperature to 350°F.
- Put sun-dried tomatoes into small bowl, and cover with hot water.
- Cover with plastic wrap, and let stand until tomatoes are plump, about 30 minutes.
- Drain well, and chop. Set aside.
- Meanwhile, steam potato quarters until tender, about 15 minutes.
- Transfer to small bowl, and let cool slightly.
- Mash potato quarters with fork, then add milk and stir until smooth. Set aside.
- Finely chop enough mushroom stems to equal ⅓ cup, and set aside.
- Reserve remaining stems for another use; store them in refrigerator up to 3 days.
- In large skillet, heat oil over medium heat.
- Add onion, garlic and red pepper flakes, and cook, stirring often, until onion begins to brown, about 10 minutes.
- Add sun-dried tomatoes and chopped mushroom stems, and cook, stirring often, scraping bottom of pan occasionally, 2 to 3 minutes.
- In medium bowl, mix all ingredients except mushroom caps.
- Mixture should be moist but hold its shape well.
- Add small amounts of water if mixture is too dry.
- Season with salt to taste (filling can be made ahead and refrigerated up to 2 days. Return to room temperature, and moisten with additional water if necessary before proceeding).
- Coat shallow baking dish with nonstick cooking spray.
- Spoon filling into mushroom caps, mounding slightly.
- Arrange mushrooms in prepared baking dish (mushrooms can be prepared up to this point and refrigerated, covered, for 1 day).
- Bake until mushrooms are tender when pierced with fork and filling is heated through, about 20 minutes.
- Serve warm or at room temperature.