In a bowl, mix together the grated carrot (soak out the moisture on a paper towel first) with the rest of the ingredients. Season with salt and pepper. Transfer to a food processor until well combined.
Shape the mixture into small balls (this recipe should make 6 golf-ball-sized falafels).
Heat a little oil in a frying pan on a medium heat. Fry the falafels, turning frequently until golden brown (5-10 minutes).
Finely chop the coriander, mint and cucumber and place in a serving bowl.
Add the yoghurt, garlic-infused oil and lime juice and mix well.
Serve with the carrot falafels.