Heat the oil in a large pot over medium heat. Add the onion, celery and carrots and fry, stirring occasionally, until the onion is soft and transparent.
Add the garlic and fry for another 2 minutes, stirring frequently.
Add one tablespoon of the flour and stir it in for about 20 seconds. Then add the second and stir it in for 20 seconds before adding the third and stirring for 20 seconds.
Add the potatoes, stock, plant-based milk, salt and thyme. Raise the heat to bring the pot to a boil then reduce the heat to a simmer and cook until the potatoes are tender - about 10 - 15 minutes.
Remove the pot from the heat and add the coconut milk. Blend a bit of the soup either with a couple pulses of an immersion blender or by transferring a couple ladles of the soup to a stand blender. You can adjust the consistency to your liking by how much you blend it, whether you prefer it quite chunky or more smooth.