1. Preheat oven to 375 degrees. In a large pot, cover sweet potatoes with cold salted water by 1 inch and bring to a boil. Reduce to a rapid simmer and cook until tender, 10 to 12 minutes.

2. Drain potatoes in a colander and let sit 5 minutes, then transfer to a food processor and process until smooth. Add coconut milk and lime zest and juice; process until combined. Transfer mixture to a 2-quart baking dish. Top with marshmallows and coconut and bake until toasted and golden, about 15 minutes.