Place the kale, chopped garlic clove, lemon juice, 2 tbsp oil and 1 tbsp water in a blender and whizz to a paste. Add some freshly ground black pepper and transfer to a bowl.
Heat 1 tbsp oil in a large wok or non-stick frying pan over a medium heat. Add the crushed garlic and the cabbage and stir-fry over a high heat for 6-7 minutes until the cabbage is just tender. Serve with the kale pesto and walnut pieces.