1. Preheat oven to 450ºF. Line a large baking sheet with parchment paper.
2. Add shredded zucchini to a large bowl and let sit 10-15 minutes. Drain excess water from zucchini bowl. Using a tea towel or several sturdy paper towels, add in 1/2 cup of zucchini into towel and wring dry. Repeat with remaining zucchini.
3. Add in eggs, flour, shredded Parmesan cheese and pepper. Mix until all ingredients are thoroughly combined.
4. Divide zucchini batter evenly into four servings and place on baking sheet lined with parchment paper. Using a spatula, thin and spread out the divided batters to form four bread squares measuring 4.5 inch x 4.5 inch x 1/4 inch.
5. Bake in oven for about 15 minutes or until surface starts to turn a light brown. Gently, using a spatula, flip breads over and cook an additional 10 minutes or until the tops of the breads are a light brown.
6. Remove from oven and flip breads again. The side on top should now be crispy. The underside will be slightly softer but this will be the inner bread sections where you will place the cheese.
7. Place one thick cheese slice in between two zucchini breads. You can then cook these the traditional way, spreading some butter or mayonnaise on the outer bread surfaces and heating them on a skillet until cheese is melted.