Heat olive oil in a large pot over medium heat and sauté the diced onion for 5 minutes until softened.
Add the minced garlic and ground cumin, cooking for 1 minute until fragrant.
Add the corn kernels and broth to the pot, bring to a boil, then reduce heat and simmer for 15 minutes.
Reserve 1 cup of corn kernels for texture, then blend the remaining soup until smooth using an immersion blender or regular blender.
Return the soup to the pot, stir in the reserved corn kernels and milk, and heat through for 2-3 minutes.
Season with salt and pepper to taste, and serve hot garnished with fresh chives and a light drizzle of olive oil.