Peel the carrots and cut into thin slices. Clean the leek and cut into thin rings.
Squeeze the garlic clove with the back of a knife and fry it whole with the carrot slices in 1 teaspoon of oil until they are a little soft. Then add the leek rings and fry for a few minutes. Dust with vegetable stock and the spices and deglaze with coconut milk, milk and water. Let the whole thing boil down a little and then serve with the rice.