In a large bowl, combine the frisee, baby arugula, green leaf lettuce, and red leaf lettuce and shredded carrots, sliced radishes, and sliced onions. Add 1/4 cup of the dressing, season with salt and pepper, and toss well. Taste the greens, and adjust seasoning with more salt, pepper, or dressing as needed (you may not need all of the dressing).
Divide the salad between four salad plates. Scatter the shaved Parmigiano and croutons evenly over all four salads.
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