Dice the fennel and mushrooms then warm the oil in a medium-sized pot over a medium heat.
Add the fennel and cook for approximately 5 minutes, stirring now and then, until the fennel starts to soften. Add the mushrooms and cook another 5 minutes until mushrooms are soft. Add the stock, bring to a simmer, cover and simmer around 10 minutes.
Remove from the heat, blend then add the coconut milk and mix through. Serve with a dash of cayenne on top.
Notes
I find the easiest way to blend soups like this is with an immersion/stick blender (affiliate link).