Peel the potatoes and put in a medium saucepan. Cover with cold water, add a few pinches of salt and bring to a boil over high heat. Lower the heat to a simmer and cook for 15 minutes, until just tender. Drain the potatoes and run cold water over them to stop the cooking process.
Heat the olive oil in a large sauté pan over medium-high heat, and add the onion, sugar and a generous pinch of salt. Cook, stirring frequently, until the onion softens and begins to brown, about 5 minutes. Add the lamb and cook, stirring occasionally, until browned, about 5 minutes. Stir in the rosemary, vinegar, about a teaspoon of salt and a few grinds of black pepper and cook for another minute. Stir in 3/4 cup water and reduce the heat so that the mixture is simmering. Cover partially and cook until most of the liquid had reduced, and the lamb is tender, about 20 minutes. Taste and add more salt and pepper if necessary. Off the heat, fold in the mint and lemon zest. Brush a TK baking dish with 1 tablespoon of the melted butter and spoon the lamb into it.
Heat the broiler. Finely slice the cooled potatoes into rounds and arrange them in layers in concentric circles over the top of the lamb. Brush the potatoes with the remaining melted butter, season with a little salt and pepper and put under the broiler until golden brown, watching carefully, about 3-5 minutes. Serve immediately.