Whisk 1 tbsp cider vinegar with 3 tbsp lemon juice, 1 tbsp olive oil and 1 tsp honey in a large bowl. Add 4 cups shredded kale and 1 grated carrot. Toss well. Refrigerate 1 hour.
Preheat oven to 450F. Cut 4 slices of whole-wheat bread into 1/2-in. cubes. Spread on a large baking sheet. Toss with 1 tbsp cider vinegar and 1/2 tsp dried basil. Bake in centre of oven until croutons are golden brown, 5 to 7 min. Sprinkle over kale salad.