In an Instant Pot, add enough olive oil to coat the bottom of the pot. Select Sauté, and when the oil is hot, add the onion. Cook, stirring occasionally, until the onion is soft and translucent, about 5 minutes. Add the garlic and ginger, and cook until fragrant, about 2 minutes more.
Add the carrots to the Instant Pot, and season with salt and pepper. Stir in the stock. Secure the lid and seal the pressure release valve. Select the Pressure Cook setting at High Pressure and set the cook time to 10 minutes.
When the timer goes off, Quick Release the pressure valve, then carefully remove the lid. Using an immersion blender, blend until the soup is smooth and creamy. (Alternatively, or if the inner pot is nonstick, transfer the soup in batches to a blender, using a dish towel to cover the open blender cap to allow steam to release.
Once the soup is pureed, stir in the coconut milk and taste for seasoning. Serve with a drizzle of coconut yogurt and cilantro if desired.
