Peel and finely chop the garlic. Scrape the peel from your turmeric. Finely chop or grate the turmeric. Peel and grate a 1cm thick chunk off the ginger. Finely slice the chilli, discarding the seeds and white bits for less heat.
Warm a large frying pan or wok over a low heat for 1 min. Add 1 tbsp oil, the garlic, turmeric, ginger and most of the chilli to the pan. Cook for 2 mins, just till softened. Add the coconut milk and 200ml boiling water. Simmer for 5 mins.
While the coconut milk simmers, coarsely grate the courgettes. Add them to the soup. Simmer for 5 mins to soften the courgettes.
Add most of the mint leaves to the soup and use a hand-held blender to blend till smooth (or ladle everything into a blender and blitz). If the soup is too thick, add a splash of water or vegetable stock. Taste. Season with salt and pepper, as needed.
Warm 1/2 tbsp oil in a separate frying pan and add the remaining chilli. Fry for 1-2 mins, aromatic. Use to garnish the soup, along with the remaining mint leaves.