1. Put the potatoes in a medium saucepan of salted water. Bring to a boil, reduce the heat, and cook at a gentle boil until tender, about 30 minutes. Drain.
2. Meanwhile, light the grill. Coat the portobello caps with 2 tablespoons of the cooking oil and sprinkle with 1/4 teaspoon of the salt and 1/4 teaspoon of the pepper. Grill the portobellos, turning, until browned and just done, about 15 minutes. Remove.
3. Coat the hens with the remaining 2 tablespoons cooking oil. Sprinkle with 1/2 teaspoon of the salt and 1/4 teaspoon of the pepper. Grill over moderate heat for 12 minutes. Turn and cook until just done, about 12 minutes longer.
4. When the potatoes and portobellos are cool enough to handle, peel the potatoes and cut them and the portobellos into 1/4-inch slices. Put them in a large bowl and add the olive oil, garlic, parsley, and the remaining 1/2 teaspoon salt and 1/4 teaspoon pepper. Mound on plates and top with the hens.
Test-Kitchen Tip: We like extra-virgin olive oil in this potato salad, but sometimes it's so powerful that it overwhelms the potatoes. If yours is strong, mix it half and half with a less exalted oil.
Wine Recommendation: The clean, minerally taste of a chardonnay-based Mâcon-Villages or St-Véran from Burgundy will highlight the hens and potatoes.