Preheat the oven to 375 degrees F. Line a sheet tray with a silicone mat. Make 4 even, very thin circles of Parmigiano on the mat. Be sure that the circles are not touching. Bake 7 to 8 minutes or until the cheese has melted, turned golden brown and looks like lace. Remove the tray from the oven and let the crisps cool for about 1 minute. Using a spatula, remove the crisps from the silicone mat and reserve on a plate.
For the salad:
Fill your sink with cool water. Toss in all the salad greens and gently swish until all the dirt and grit falls to the bottom of the basin. Gently lift the greens out of the water and put in a salad spinner. If the greens are especially dirty empty the sink, rinse to rid of dirt and repeat the process. Spin the greens until they are dry and still very fresh looking. If not using the greens right away, store them wrapped loosely in paper towels then sealed in plastic bags in the crisper drawer of your refrigerator.
In a large bowl, place the greens and herbs. Add the tomatoes, onions, and cucumbers. Drizzle in half of the oil and vinegar and season with salt. Using your hands, gently toss the salad to combine. Taste! Add the remaining oil and vinegar, if needed and season again with salt, if needed (you probably will). The salad should be very flavorful but not soggy.
Arrange the salad on individual salad plates or bowls. Sprinkle each salad with the nuts and garnish with a Parmigiano crisp.