Heat the oil over medium heat in a large soup pot.
Add the onion and garlic and cook, stirring until softened, about 5 minutes.
Add the squash, broth, curry powder, and salt and bring to a boil.
Reduce the heat to a medium-low and simmer until the squash is tender, about 15 minutes.
Remove the soup from the heat, stir in the honey, and puree until smooth in the pot using an immersion blender or in two batches in a regular blender.
Taste and season with salt, if necessary.
To serve, ladle the soup into serving bowls and drizzle with the yogurt.