In a large skillet, heat the EVOO, 2 turns of the pan, over medium-high heat. Add the lamb and cook to brown well, 7 to 8 minutes. Add the onion, ginger and garlic; season with salt and pepper. Stir in the turmeric, cumin, coriander and chili powder. Cook, stirring occasionally, until the onion is softened, about 5 minutes. Stir in the tomato sauce and honey, lower the heat and simmer until ready to serve.
Preheat the broiler. Melt the butter over low heat in a small saucepan or in the microwave on high for 1 minute. Toast the rolls under the broiler until golden. Liberally brush the rolls with the melted butter. Layer the roll bottoms with the sloppy joe meat, cilantro, mint, shallots and toll tops.