Preheat the oven to 450 degrees F. Put the potatoes in a large pot and cover with cold water by 1 inch; season with salt. Bring to a boil and cook over medium-high heat until just tender, about 7 minutes; drain.
Meanwhile, pulse the bread in a food processor to make coarse crumbs; combine with the olive oil, garlic, lemon zest, 1 teaspoon salt and a few grinds of pepper in a large bowl. Add the potatoes and toss.
Arrange the potatoes cut-side down on a baking sheet. Roast until golden and tender, about 10 minutes. Sprinkle with the parsley and parmesan; continue roasting until golden brown, about 5 more minutes. Transfer to a serving dish, season with salt and serve with lemon wedges.