1. Preheat the oven to 400°F.
2. Place the mushrooms in a large bowl. Season them generously with salt and pepper and drizzle with 2 tablespoons olive oil. Toss until the mushrooms are lightly coated with oil. Arrange the mushrooms, stem side down, on a baking sheet and roast until deep golden brown and tender, about 15 minutes, remove and cool the mushrooms.
3. Place the potatoes in a large saucepan of cold water. Add ½ teaspoon of salt and bring to a boil. Cover, reduce the heat, and cook until the potatoes are tender but still firm when tested with a paring knife, about 30 minutes, depending upon their size. Drain and let stand just until cool enough to handle.
4. Cut the mushroom caps into quarters and place in a large bowl. Add the spinach and radishes. Combine 6 tablespoons of the remaining oil, vinegar, mirin, soy sauce, and parsley in a small jar with a tight-fitting lid. Shake vigorously to mix and pour over the spinach mixture. Toss well, cut the potatoes into ½-inch dice, add to the bowl, and toss well. Cool to room temperature.
5. Heat the remaining 2 tablespoons olive oil in a very small skillet or saucepan over low heat. Add the garlic and cook, shaking the skillet occasionally, until the garlic is golden brown, about 2 minutes. Spoon the garlic and oil over the salad.
6. To serve, place the sesame seeds and peppercorns in a peppermill and grind a generous amount over the salad. Or place the sesame seeds and peppercorns on a flat surface and crush them lightly with the bottom of a small, heavy saucepan, then sprinkle the mixture over the salad. Toss the salad lightly and serve.