Heat the olive oil in a large Dutch oven over medium heat. Add the squash and leeks and season with 1/4 teaspoon salt; cook, stirring occasionally, until the leeks start softening, about 3 minutes.
Add the curry powder, ginger and lime zest and stir to coat. Reduce the heat to medium low and add 1 cup water. Bring to a simmer, then cover and cook until the squash is almost tender, about 5 minutes.
Add the heavy cream to the pot, then stir in the mussels. Increase the heat to medium, cover and simmer until the mussels open, 5 to 6 minutes. (Discard any unopened mussels.) Stir in the lime juice and cilantro. Serve with the bread.