Heat the olive oil in a large pot over medium heat. Add the diced onion and cook until it softens, about 5 minutes.
Stir in the minced garlic and grated ginger. Cook for 1 minute until fragrant.
Add the cubed butternut squash, vegetable broth, salt, and black pepper. Bring the mixture to a boil, then reduce heat and simmer until the squash is tender, about 20 minutes.
Remove the pot from heat. Use an immersion blender to puree the soup until smooth.
Return the pot to low heat and stir in the coconut milk. Warm the soup through without boiling.
Ladle into bowls and top with cilantro. Serve with lime wedges on the side.