Preheat the oven to 400 F/ 200 C/ gas mark 6. You will need a 6-cup muffin tray.
Spiralize the courgette, season and combine with the cheese in a large bowl. Set aside.
Peel and spiralize the potatoes. Place on 2 sheets of paper towel and toss gently to get rid of excess water.
Using a large non-stick frying pan (a pancake pan works well) heat up the oil and fry the spiralized potato over a medium heat for approx. 3 minutes, stirring all the time with 2 forks or tongs. Remove from the heat, season and add to the bowl. Mix well with the courgette (break the long 'spaghetti' if you have to).
Fill the muffin tray with the mixture, pressing gently and ensuring there is a little more mixture around the edges than in the middle. Crack the eggs and carefully pour one by one into each nest ensuring the yolk is in the middle. Season and bake for 15-20 minutes (depending on how you like your eggs).
Remove from the oven, run a knife around the edges of the nests and using a spatula take out the nests and place on individual plates. Sprinkle with freshly chopped chives, drizzle with your favourite sauce (ketchup works well) and serve with sliced avocados or simply on their own.