If the head of escarole is large, use half for the salad and store half in a resealable bag in the refrigerator for another recipe.
Combine the escarole and radicchio in a large salad bowl. Toss in the dates.
In a jar with a tight-fitting lid, combine the lemon juice, mustard, grated Parmesan cheese, olive oil, and black pepper. Shake well to combine. Pour over the salad and toss.
Grate more Parmesan on top and serve.