Preheat oven to 450℉. Toss the cauliflower with oil and curry powder. Spread cauliflower on a baking sheet covered in parchment paper. Reserve 1 tablespoon of cauliflower.
In a large pot, add oil, onion, and garlic. Cook over medium heat until onions are translucent and soft.
Add the vegetable broth, remaining roasted cauliflower, coconut milk, red curry paste, salt, lime juice, and coriander. Heat over medium heat for 15-20 minutes.
Puree the soup with a hand blender or in small batches using a regular blender. Place the soup back on the stove and bring to a boil.
In a small bowl, combine the cornstarch and cold water. Stir to combine. Add to the soup and stir. Cook for 5 minutes over high heat.