Rinse the mussels in a colander under cold water, scrub the shells thoroughly, remove the tough, wiry beards, and discard any mussels with broken or gaping shells. While the mussels drain, heat the oil in a large, wide pot over medium- high heat. Add the carrot and jalapeño and sauté, stirring occasionally until they begin to soften and lightly brown, about 2 min. Add the garlic and 1/2 tsp. of the lime zest, and continue to sauté until fragrant, 30 seconds. Pour in the wine and raise the heat to high. As soon as the wine boils, add the mussels and cover the pot. Steam the mussels, shaking the pot once or twice, until the shells open, 5 to 6 min.
Remove the pot from the heat. With a slotted spoon, transfer the mussels to a large bowl and keep warm. Return the pot with the cooking liquid to the heat, add the cream, and boil until the sauce reduces just a bit, 2 to 3 min. Add 1-1/2 Tbs. of the lime juice, the cilantro, and the chile sauce, if using. Taste and add more lime juice and salt if needed. Ladle the mussels into wide, shallow bowls, pour some of the sauce over each portion, and serve immediately.