Heat a heavy-bottomed pot over medium-low heat. Add the olive oil followed by the onions. Cook until the onions are fragrant and translucent, 4 to 5 minutes. Stir in the squash, potato, and carrot. Continue to cook for until the squash begins to soften, 5 minutes or so. Stir in the garlic, cook for a minute then add in all the spices, cooking for another minute more.
Add the wine, scrapping up any pieces stuck to the bottom. Allow some of the wine to cook out then measure in the vegetable broth. Bring to a boil, reduce to a simmer, and let cook until the potatoes are tender, 10 to 15 minutes.
While the soup simmers, heat 2 tablespoons of the oil in a frying pan on medium high. Add the collards and cook, stirring, until the collards become bright green and tender. Remove them from the heat and set aside.
Puree the soup using a blender or an immersion blender. Add in the coconut milk and continue to heat the soup until hot. Taste and add salt as needed (usually depends on how salty the broth is). Divide into two bowls and top with a drizzle of coconut milk, sprinkle of paprika.