WHIRL cauliflower in a food processor until it looks like rice (it should measure 4 cups). Whisk eggs with garlic and oregano in a medium bowl. Stir in cauliflower and mozzarella. Transfer to a parchment-lined baking sheet. Form into a 9 x 11-in. rectangle and smooth top with a rubber spatula. Bake at 450F until golden and crispy around edges, about 30 min.
REMOVE from oven and cut in half lengthwise. Cut each half into 3 rectangles. Top each of 3 portions with 1/2 cup grated cheddar. Sandwich with remaining cauliflower crusts.