Grate the carrots in a food processor, then place into a large bowl with the chives.
Add in the eggs and the gluten free flour to bind everything together, followed by the feta cheese (it will melt and again will help to hold the fritter together).
For a touch of luxury, some lactose free cream and stir well, seasoning to taste with salt and freshly ground black pepper.
Just before you fry it's worth just squeezing some of the mixture together in your hands to ensure it won't fall apart when cooking.
If you think it will, just add either a little more beaten egg or gluten free flour, only just enough to stick them together.
Heat a large frying pan, add in the oil and form the mixture into thin fritters, so they will cook quickly.
Fry for 4-6 minutes until golden-brown on both sides. Remember the golden rule of frying - don't play with the food too much, let the fritters form a crust before you turn them over. Serve straightaway scattered with more chives.