Begin by peeling and shredding the carrots using a box grater or a food processor. Set them aside in a large mixing bowl.
Next, slice or shred the apples, making sure to remove any seeds and cores. Once sliced, squeeze out excess juice from the grated apples using paper towels to prevent the salad from becoming soggy.
Add the shredded apples to the bowl with the carrots. Chop the green onions and cilantro, and mix them into the bowl as well. If desired, add currants or raisins for a touch of sweetness.
In a small bowl, whisk together the cider vinegar or lemon juice, Dijon mustard, kosher salt, and pepper. Gradually whisk in the olive oil or mayonnaise until the dressing is smooth and emulsified. Taste and adjust with honey or sugar for sweetness if desired.
Pour the dressing over the salad mixture and toss everything to coat evenly. Allow the salad to sit for at least 30 minutes to let the flavors blend.
Before serving, garnish the salad with chopped chives or parsley for an added burst of flavor. The salad can be served cold or at room temperature.