In a large stockpot or dutch oven, heat the olive oil over medium heat. Add the sliced onion, salt, pepper, and cook for about 4 minutes to soften the onion.
Add the carrots, stir well, and cook for other 5 minutes.
Add the garlic and turmeric, stir well, and cook for another minute or two.
Add the broth, coconut milk, and bring to a boil.
Reduce the heat to a simmer and cook for about 20 until the carrots soften, stirring occasionally.
Remove the pot from the heat and let it slightly cool.
Transfer soup to a blender. Blend until smooth, or blend it with an immersion blender, taste, and adjust seasoning as needed.
Serve hot or, to serve cold, place in a container in the refrigerator for at least 2 hours.