Preheat the oven to 425 degrees F and line a baking sheet with parchment paper or a silicone mat.
Rice the cauliflower by cutting the head into florets. Pulse the florets in a blender or food processor until it is in small crumbs. Spread out the riced cauliflower on the baking sheet.
Roast for 20 minutes and then remove from the oven. Cool completely (about 15 minutes). Remove the excess moisture by placing the cauliflower on a paper towel or kitchen towel and squeezing and twisting as much as possible.
In a large bowl, mix together the riced cauliflower, mozzarella, parmesan, eggs, garlic, basil, parsley, salt, and pepper. Once combined it should hold together when formed.
Place a large skillet over medium heat and melt 2 tablespoons of butter. (see note) Place half of the cauliflower mixture into the skillet and for it into two squares, about 1/2-inch thick each. (If you have a really large skillet, you can form 4 squares using all of the mixture.)
Cook the cauliflower bread for 7-10 minutes on each side until a nice crust forms. Then add 2 cheese slices to one half of the bread squares. Cover with a lid and allow the cheese to melt.
Place the "bread" slices with cheese onto a plate and then top with the other "bread" slice on top. Repeat with the other grilled cheese. Serve warm.
Notes
If your skillet will hold only one cauliflower bread rectangle at a time you will need 4 tablespoons of butter for each half of the cauliflower mixture. It will also take another 20 minutes of cooking time.