Staying away from potatoes is perhaps the hardest thing with low carbing, I think. So when I find a recipe that not just sufficiently replaces the glorious spud version but actually surpasses it I get filled with joy.
Found the original recipe in the great cookery book 1001 Low Carb Recipes where it is called Kolikythia Krokettes. As said in the book, they go remarkably well with grilled chicken.
It is important to get most of the water out of the grated courgette, and then use lots of butter while frying on a medium heat for a long time to get a nice crispy surface.
Ingredients for two people
2 medium courgette (zucchini), grated
1 tsp salt
2 eggs
100 gram finely crumbled feta cheese
1 tsp dried oregano
1/2 yellow onion, finely chopped
1/2 tbsp flour
black pepper, to taste
butter
Original recipe calls for 3 tbsp protein powder. Assuming it was to provide some binding for the frying we simply used a bit of flour instead. Worked fine.
Method
Put the grated courgette in a bowl and mix with the salt. Leave it for half an hour to an hour, then drain and squeeze as much of the liquid out as you can.
Add onion, feta, oregano, pepper, eggs, flour and mix it together.
Melt a tablespoon of butter in a non stick frying pan. Use a spoon to get just over a tablespoon's worth of courgette mix for each croquette and place in the pan.
The patties will absorb some butter, add more as needed.
Leave the patties to really brown on the bottom before turning them once and finish frying on the other side. Properly browned you get a nice, toasty flavour and a crisp outside texture that goes so well with the silky inside.
Delicious. I think these are even tastier than potato rösti, and the texture is so smooth. Serve with bacon, or sausages, maybe lamb, or why not sticky BBQ chicken wings...
If you are in a hurry and don't want to fiddle with frying a number of qroquettes, just make one big patty in the frying pan. Fry until browned, place a plate over the frying pan and turn upside down to get the patty out, then slide back in the pan and fry the other side.

Courgette patties frying away. Don't worry if they are a bit loose, just remember to leave them to fry for a long time so the bottom goes crispy. Spooning some of the melted butter over the top while frying helps keeping them together when flipping.

Finished result. Crispy, toasty outside with a silky smooth inside tasting very much like potato röstis only better...