Trim and dice the courgettes. Trim the dry tips off the fennel, saving any fronds for garnishing. Dice the fennel. Peel and finely chop the onion.
Place a large pan on a medium heat for 1 min. Add 1 tbsp olive oil, the chopped veg and a pinch of salt. Cook for 8 mins, stirring often, till the veg have softened and lightly coloured.
While the veg cook, peel and chop the potatoes into small dice.
Fill and boil your kettle. When the veg have cooked for 8 mins, add 2 tsp fennel seeds to the pan. Cook for 1 min, stirring. Add the potatoes and stir. Pour in 600ml boiling water. Pop a lid on the pan and simmer for 15 mins till the potato is tender.
While the soup simmers, zest and juice the lime, keeping the juice and zest separate. Crumble the feta. Roughly chop the mint leaves.
When the veg are tender, add the lime juice and all but a few pinches of the mint leaves. Blend the soup with a hand-held blender till smooth and creamy, or whizz it in batches in a blender.
Stir through half the feta. Taste and add a pinch of salt or pepper if needed. Ladle the soup into warm bowls. Top with the remaining feta, the lime zest, mint leaves and any fennel fronds.