Preheat the oven to 350°F.
In a food processor or blender, pulse the broccoli until roughly chopped (don’t overprocess—you want it to still be rough).
Transfer to a microwave-safe bowl, and microwave on high for 2 minutes. Allow to cool for a few minutes, and then twist in a thin cloth or cheesecloth to remove any water (not a lot will come out, but the little that’s there needs to be removed).
Transfer the broccoli to a medium bowl.
In a small bowl, whisk together the eggs, garlic, shallot, chives, oregano, and parsley, and season with salt and pepper; pour over the broccoli, and mix until well incorporated.
Line a large baking sheet with parchment paper, and scoop the broccoli mixture into four equal sections.
Spread each section of broccoli out until it’s about ¼ inch thick, leaving a little room in between each.
Bake for 10 minutes, and then flip and bake for another 7 minutes.
Remove the baking sheet from the oven, and allow the broccoli wraps to cool. Store in the refrigerator. To reheat, broil them quickly in the oven or toaster oven.