Step 1
Cut cauliflower into medium-sized florets and process in batches in a food processor. For each batch pulse until pieces break down and continue processing until texture resembles rice grains. Transfer to a large pot. Sprinkle with kosher salt. Cook over medium-high heat stirring until mixture is wet and soft about 30 minutes. Reduce heat if it begins to brown. Remove from heat and allow cauliflower to cool.
Step 2
Transfer cauliflower in batches to a clean cotton towel. Bring up sides twist towel and squeeze out as much liquid as you can. For this recipe you should have about 3 1/2 cups cooked squeezed-dry cauliflower.
Step 3
Preheat oven to 350 degrees F (175 degrees C). Line a large rectangular baking dish with parchment paper allowing ends to extend up over the sides for easy lifting. Lightly brush parchment with olive oil.
Step 4
Crack eggs into a large mixing bowl. Add crushed garlic oregano pepper and cayenne pepper; whisk together. Transfer cauliflower to mixing bowl. Add shredded Cheddar cheese and grated Parmigiano-Reggiano. Mix thoroughly. Transfer to prepared baking dish. Tamp down and smooth out evenly.
Step 5
Bake in preheated oven until deeply golden brown about 1 hour. Allow to cool to room temperature. Cover and refrigerate until thoroughly chilled 3 or 4 hours.
Step 6
Preheat oven to 400 degrees F. Line a baking sheet with a silicone mat; lightly oil the mat.
Step 7
Lift cauliflower out of pan. Slice in half lengthwise; slice each half crosswise into thin \fries\ about 1 inch wide. Arrange fries on the mat so they do not touch; brush lightly with olive oil. Sprinkle with a dusting of grated Parmigiano-Reggiano cheese.
Step 8
Bake in preheated oven until deeply browned about 20 to 25 minutes. Allow to cool slightly before serving.