Wash the carrots, halve any larger ones, then place in a large cold non-stick frying pan with 1 tablespoon of olive oil and a pinch of sea salt and black pepper. Put on a medium-high heat for 15 minutes, or until golden and tender, tossing regularly.
Meanwhile, halve the pomegranate, squeeze the juice from one half through a sieve into a large bowl, add 1 tablespoon of red wine vinegar and 2 teaspoons of extra virgin olive oil. Finely chop the top leafy half of the mint (reserving a few nice leaves), stir into the bowl, then taste and season to perfection.
Transfer the carrots to the dressing bowl, while you toss the grains in the pan for 1 minute with a splash of water to warm through. Tip into the bowl and mix with the dressed carrots, then divide between your plates.
Holding the remaining pomegranate half cut-side down in your fingers, bash the back of it with a spoon so all the seeds tumble over the salads. Crumble or grate over the feta, sprinkle over the reserved mint leaves, and tuck in.