Zest the lemon. With a sharp knife, remove the white pith. Put the inner part of the lemon into a food processor.
Add the basil, fennel seeds, the fluffy fennel greens from the stalks, 4 tablespoons of olive oil. Puree. Gradually add the 5th tablespoon of olive oil, if needed.
Now add the lemon zest, honey, salt, and pepper to the dressing. Puree again. You can make this a few hours ahead of time, and chill in the refrigerator, if needed.
Grate the parmesan or pecorino cheese. Line a baking sheet with parchment. Arrange the gratings to the baking sheet in little flat 2-inch circles.
Broil these parmesan disks in the oven until they melt and turn into little disks.
Arrange the arugula in a large bowl or a wide platter.
Use a sharp vegetable peeler to shave the fennel bulb. Add the fennel shavings to the salad.
Top the salad with the dressing and disks of broiled cheese.