Preheat oven to 220C. Combine chickpeas and 2 tbsp olive oil in a bowl, season generously and spread on an oven tray lined with baking paper. Roast, shaking occasionally, until browned and crisp (15-20 minutes).
Meanwhile, combine fennel, carrot, coriander, flour, egg, cumin and spring onion in a bowl, and stir until mixture just comes together. Stir in feta and season to taste.
Heat half the remaining oil in a frying pan over medium heat, add ⅓-cup portions of fritter mixture in batches and fry, turning once, until golden brown and cooked through (4-5 minutes), wiping out pan with paper towels and adding remaining oil between batches.
Scatter fritters with chickpeas, extra coriander and mint, and serve warm with yoghurt and lemon wedges.
