Bring a large pot of salted water to a boil over high. In separate batches, cook the vegetables (in this order: haricots verts, zucchini, eggplant, and sweet potato) until each vegetable is almost al dente, 1 minute and 30 seconds for haricots verts, 2 to 3 minutes for zucchini and eggplant, and 6 to 8 minutes for sweet potatoes. Drain vegetables, and transfer to a baking sheet; set aside.
Heat oil in a large Dutch oven over medium. Add onion, garlic, ginger, salt, and black pepper; cook, stirring occasionally, until onion is softened, 5 to 6 minutes.
Stir in coconut milk, scraping bottom of Dutch oven to remove any browned bits. Bring to a boil over medium-high. Fold in spinach until it begins to wilt, about 1 minute. Stir in reserved vegetables. Bring to a simmer over medium; cook, stirring occasionally, until flavors meld, about 15 minutes. Remove from heat; stir in cilantro, mint, scallions, lime juice, and sambal oelek. Season with salt and black pepper to taste. Garnish with cilantro and mint leaves; serve with rice and lime wedges.
