In a small bowl, combine the vinegar, mustard, honey, and salt. Slowly drizzle in the extra virgin olive oil and whisk until emulsified. Taste for seasoning and add additional salt or honey until the dressing tastes balanced.
Chop the lettuce and radicchio. Place into a colander and rinse throughly under cold running water. Dry in a salad spinner.
Thinly slice the fennel and radishes using a sharp knife or vegetable mandoline.
Toss the chopped lettuce and radicchio with the fennel and radishes.
Portion the salad onto side plates and season with cracked black pepper to taste. Drizzle with dressing to taste, then top with parmesan cheese. Serve immediately. This salad keeps undressed in the fridge for up to 3 days. To preserve crunchiness, store in a loosely covered container layered with pieces of paper towel to absorb moisture.