Trim and peel the butternut squash. Halve, remove the seeds, and cut the flesh into ¾-inch chunks (about 4 ½ cups). If using pre-cut butternut squash, use 1 ½ pounds and cut down any pieces that are larger than ¾-inch.
Heat vegetable oil in a large saucepan or medium pot over medium heat until shimmering. Add diced yellow onion and ¼ teaspoon of the kosher salt. Cook, stirring occasionally, until softened, 6 to 8 minutes.
Stir in Thai red curry paste and minced garlic. Cook, stirring often, until fragrant, about 1 minute. Stir in the coconut milk and granulated sugar if desired, increase the heat to medium high, and bring to a boil.
Stir in the butternut squash, drained chickpeas, and remaining kosher salt. Bring to a simmer. Cook, stirring occasionally and reducing the heat as needed to maintain a simmer, until the squash is tender and cooked through, 15 to 25 minutes.
Stir in the coarsely chopped kale leaves and simmer until the kale is tender, about 5 minutes.
Remove the saucepan from the heat. Stir in lime juice. Taste and season with more kosher salt as needed. Garnish with coarsely chopped fresh cilantro leaves and serve over rice and with lime wedges if desired.