Cook honey and balsamic together over medium-high heat in a large saute pan, about 5 minutes. Toast walnuts in a small skillet; set aside to cool.
Pile greens on a platter. Stir mustard into balsamic-honey dressing, then whisk in about 1 cup extra-virgin olive oil; pour over greens. Season greens with salt and pepper and garnish with walnuts, pomegranate seeds, shavings of Parmesan, and shallot.