Toast walnuts and set aside.
Remove carrot greens, chop finely. Pick and chop mint leaves and ginger.
In a food processor, pulse walnuts, ginger, garlic (reserve ⅓), carrot tops, mint, half olive oil, 2 tbsp oxymelo vinegar, and salt into a pesto.
Pare carrots; slice into ribbons using a mandolin or spiralizer.
Toast and grind cumin, fennel, and caraway seeds. In a bowl, whisk with remaining garlic, salt, oxymelo, and olive oil to make dressing.
Combine carrots, pesto, and dressing. Toss gently and serve.