Whisk the eggs: In a bowl, whisk together 3 large eggs with 1 tablespoon finely chopped fresh parsley, salt, and black pepper until well combined and slightly frothy, about 1 minute.
Heat the skillet: Place a non-stick or cast-iron skillet over medium-high heat and add a light coating of neutral oil, swirling to coat evenly, about 30 seconds.
Pour the egg mixture: Once the skillet is hot, carefully pour the egg mixture into the center and let it spread naturally, cooking for about 2 to 3 minutes until the edges begin to set but the center is still slightly wet.
Position the bread: When the eggs are just beginning to set on top, quickly place both bread slices directly on top of the omelet in the skillet, cover with a lid, and cook for 1 to 2 minutes so the bread lightly toasts on the bottom while the eggs continue to cook.
Flip the sandwich: Remove the lid carefully, slide a spatula under the bread and omelet together, flip the entire mixture so the bread side is now touching the skillet, and reduce heat to medium.
Fold and layer: Gently fold any excess omelet edges inward toward the center, creating a neat rectangle, then on one bread slice layer the mozzarella cheese, sliced ham, spinach, tomato slice, and a second slice of mozzarella cheese.
Complete and finish: Place the second slice of toast on top to form the sandwich, then cook for 3 to 4 minutes over medium heat until the bottom toast is golden and the cheese is completely melted.