Add a splash of coconut oil to a medium pot on medium heat. Add the shallot and garlic and fry gently for 1 minute. Don't let the garlic brown.

Stir the potatoes and 1/2 cup corn into the pot. Add a pinch of salt and a few grinds of black pepper, and fry for 2 or 3 minutes before adding the stock and tarragon sprigs. Bring to a simmer. Let cook for about 15 minutes, or until the potatoes are fork-tender and the liquid has reduced slightly. Take the pot off the heat to cool.

Once cooled, remove the tarragon sprigs. Use either a stand or immersion blender to blitz the soup base until no large pieces remain. Strain through a fine mesh strainer back into the pot (use a chinois if you have one). Really press down on the strainer to make sure you get all the delicious liquid out. Put the pot back on the heat, set to medium.

Add the coconut milk to the pot and whisk until smooth. Check the seasoning, and add more salt and pepper as needed. Because every brand of coconut milk is different, add a pinch of sugar to boost the sweetness if you have to. Bring the pot just to a simmer, then take it off the heat again. When cooled to room temperature, transfer the soup into a lidded container and put it in the fridge for at least 1 hour.

Serve the soup as cold as possible. To do so, put a few tbsp sweet corn in a bowl, then ladle the soup over it. Finish with a light pinch of the minced fresh tarragon.