In a saucepan over medium heat, add the oil.
Once it is hot, add in the garlic and onion. Saute these for about 3-4 minutes, until the onions are translucent. Keep the lid on the pot, stirring every 30 seconds.
Add the celery and saute for another 1-2 minutes.
In a small bowl, whisk together the cornstarch with the vegetable broth, which should be at room temperature. Whisk until no clumps remain.
Add the broccoli and the vegetable broth-cornstarch mixture into the saucepan, and stir to combine.
Cover the pot with a lid, leaving a bit of space to let the steam escape. Simmer this for about 15 minutes, until the broccoli is tender and can be easily poked into with a fork.
Blend the soup using a handle blender, adding in the coconut milk, water and salt. Blend until there are no broccoli chunks and it is smooth and creamy.
Turn the heat to medium-high, and allow it to come to a boil. Once it boils, turn the heat to low.
Taste the soup and add any other seasonings (like black pepper) as desired. Let it simmer for another 10-15 minutes to thicken to the desired consistency.
Once it's ready, remove from the heat. Pour the soup into a bowl to serve. Top with a sprinkle of croutons or a drizzle of olive oil, and enjoy!