Preheat oven to 450°F.
Combine coriander, cumin, cinnamon, turmeric, salt, pepper and cayenne in a small bowl. Toss cauliflower with 1 tablespoon oil in a large bowl, sprinkle with 1 tablespoon of the spice mixture and toss again. Spread in a single layer on a rimmed baking sheet. Roast the cauliflower until the edges are browned, 15 to 20 minutes. Set aside.
Meanwhile, heat the remaining 1 tablespoon oil in a large pot over medium-high heat. Add onion and carrot and cook, stirring often, until starting to brown, 3 to 4 minutes. Reduce heat to medium and continue cooking, stirring often, until the onion is soft, 3 to 4 minutes. Add garlic, ginger, chile and the remaining spice mixture. Cook, stirring for 1 minute more.
Stir in tomato sauce, scraping up any browned bits, and simmer for 1 minute. Add broth, potatoes, sweet potatoes, lime zest and juice. Cover and bring to a boil over high heat. Reduce heat to maintain a gentle simmer and cook, partially covered and stirring occasionally, until the vegetables are tender, 35 to 40 minutes.
Stir in coconut milk and the roasted cauliflower. Return to a simmer to heat through. Serve garnished with cilantro and chiles, if desired.
