In a large Dutch oven or heavy-bottomed pot, melt the 4 tablespoons of vegan butter over medium heat. Add the finely chopped onion, diced carrots, and diced celery, and cook for 8-10 minutes, stirring often, until the vegetables have softened and the onion is translucent.
Stir in the 2 teaspoons of minced garlic and cook for one additional minute until it becomes fragrant.
Pour in the 6 cups of vegetable broth and add the 5 diced potatoes, 1 teaspoon dried thyme, 1/2 teaspoon black pepper, and 1 1/2 teaspoons salt to the pot. Increase the heat to high and bring the soup to a boil.
Once boiling, reduce the heat to a steady simmer and cook uncovered for 20-25 minutes, or until the potatoes are very tender and can be easily pierced with a fork.
In a small bowl, whisk together the 1 cup of canned coconut milk and 1 tablespoon of cornstarch until no lumps remain to create a smooth slurry.
Stir the coconut milk slurry into the simmering soup. Continue to cook for another 5-7 minutes, stirring occasionally, until the soup has thickened slightly.
Use a potato masher to partially mash some of the potatoes directly in the pot to create a thicker, creamier texture, leaving some chunks for a hearty consistency.
Ladle the hot soup into bowls and garnish each serving with a sprinkle of chopped fresh chives.
