In a large pot of salted boiling water, cook the unpeeled whole potatoes until just tender when pierced with a small knife, about 20 minutes. Drain and let cool, then refrigerate until cold, at least 2-3 hours or up to 1 day. Peel the potatoes and cut them lengthwise into slices 1/2 inch thick. Use the center slices from each potato. (Reserve remaining slices for another use.)
Preheat the oven to 400 degrees. Spread a T. of olive oil on a baking sheet, or use nonstick vegetable oil cooking spray, if preferred.
In a heavy frying pan, heat 2 T. of olive oil over medium-low heat. Add the minced rosemary and garlic, cover, and cook until the garlic is softened but not brown, about a minute or two. Stir in the mustard, 1/2 t. kosher salt, and 1/2 t. pepper and remove from the heat. Add the bread crumbs and toss until evenly coated. Stir in the cheese.
Arrange the potato slices on a work surface. Brush the tops generously with the egg white. Spread approximately 1 T. of the crumb mixture on each slice and press to adhere and cover evenly. Place the slices, coated side down, on the prepared baking sheet. Brush the uncoated sides with the egg white. Spread the remaining crumb mixture on the slices, pressing to adhere.
Bake the potato slices until the coating on the bottom is crusty, about 8 – 10 minutes. Carefully slide a thin metal spatula under each slice and turn it over. Bake until brown on the second side, about 5 – 6 minutes longer. Transfer the potato slices to a platter, garnish with rosemary sprigs, if desired, and serve.