1. Prepare the Potato Base

1. Grate the Potatoes: Peel and finely grate the potatoes. Place them in a bowl of cold water for a few minutes to prevent browning. Drain thoroughly and squeeze out excess water with a clean kitchen towel.
2. Sauté the Vegetables: In a pan, heat 1 tablespoon of olive oil over medium heat. Add the chopped onion and sauté until translucent, about 2-3 minutes. Add the grated carrot and cook for another 2-3 minutes until softened. Remove from heat.

2. Make the Batter

1. Mix Wet Ingredients: In a large mixing bowl, whisk together the eggs and milk until smooth.
2. Incorporate Dry Ingredients: Gradually add the flour, whisking continuously to avoid lumps.
3. Combine: Stir in the grated potatoes, sautéed onion, and carrot. Season generously with salt and ground black pepper. Mix until evenly combined.

3. Cook the Potato Mixture

1. Heat the Pan: Heat 2-3 tablespoons of olive oil in a large skillet over medium heat. Ensure the oil coats the entire pan for even cooking.
2. Spread the Mixture: Pour the potato batter into the skillet, spreading it evenly to form a flat base. Cook for 5-7 minutes until the underside is golden and crispy.

4. Add the Toppings

1. Layer the Toppings: Arrange the sliced tomatoes evenly on top of the potato base. Sprinkle the grated cheese generously over the tomatoes.
2. Cover and Cook: Lower the heat to a gentle simmer, cover the skillet with a lid, and cook for another 5-7 minutes until the cheese melts and the tomatoes soften.

5. Serve the Dish

1. Garnish: Transfer the potato dish onto a serving plate. Sprinkle with chopped chives and parsley for added flavor and color.
2. Slice and Serve: Cut the dish into slices, just like pizza, and serve immediately while hot.