Place extra virgin olive oil in a large pot with minced garlic, onion, bay leaves and ginger. Bring to a medium heat and sauté the veggies until tender.
Add the butternut squash, broccoli, salt, pepper, chili powder, lime juice, and broth to the pot. Bring to a boil then reduce to a simmer.
Simmer on low, covered 20 minutes. Remove the bay leaves then stir in the milk.
Transfer the soup to a high-speed blender and blend on high until smooth. You may need to do this in batches.