Grate the carrots using either a food processor or a standard box grater. Combine in a large bowl with the chopped parsley.
In a small jar or liquid measuring cup, combine the olive oil, lemon juice, Dijon, honey, salt, and pepper. Shake or whisk well to blend. Pour over the carrots and parsley and toss well to blend. Taste and adjust seasoning if necessary. Cover and refrigerate until ready to serve.
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Notes
Another variant: You can use red wine vinegar in place of the lemon juice. Try it and see which you prefer!