Zest one lime, then cut in half. Set aside.
Heat olive oil over medium heat in a large, heavy-bottomed stock pot with a tight-fitting lid and add curry paste. Saute curry paste for about 1-2 minutes, breaking up any large clumps. Add coconut milk, broth, fish sauce and lime zest. Juice lime into the pot and allow the whole mixture to come to a boil.
Add mussels, reduce heat to medium-low and cover. Steam the mussels until they're opened, about 5-7 minutes.
While mussels are steaming, put spiralized zucchini in a large serving dish. Slice the second lime into wedges. When the mussels are done, spoon the curry sauce and mussels over the zucchini noodles, allowing the zucchini to soften a bit. Sprinkle the cilantro and basil over the mussels, then add lime wedges around the sides. Serve immediately.
Note: this dish can also be made with littleneck clams, but be sure to build in more time to steam the clams, as it generally takes longer for them to open than mussels.