1- First of all take all ingredients on your work-table. Then, fry your all potatoes (thinly sliced round shape potatoes) over medium heat till its color change to golden color in frying-pan. Then, set aside. (According to us, fried potatoes are better for this dish. But, if you want, you can use boiled potatoes or raw potatoes).
2- Meanwhile, in a non-stick saucepan, drizzle your vegetable oil and butter and add finely chopped garlic and fry till fragrant. Then, add in your chopped onions and fry for a while before adding ground beef (this process takes nearly 3-4 minutes). When your onions are translucent, add your ground beef, tomato paste and pepper paste and mix them well and cook over medium heat until its pink color disappears (this process takes another 4-5 minutes). Then, add your chopped spinach and a pinch of ground black pepper and salt and stir. One or two minutes later, add grated carrots and stir mixture. Then, turn down the heat to low and let it simmer for 7-to-9 minutes. Then, remove the spinach mixture from the heat and add egg and stir. Then, set aside.
3- Preparation of Béchamel Sauce; In a small saucepan, melt the butter. Then, add your all purpose flour and sauté over low heat till its color change to yellow (it takes 1 or 2 minutes). Stir constantly, don't stop. Then add milk and stir continuously to make your béchamel Sauce smooth and even. (Bye the way, let us to explain one thing; If flour particles do not dissolve, you can use a blender.) Lastly, add salt, red pepper flakes and ground black pepper and cook for 3 or 4 minutes. Then, set aside.
4- Preheat the oven to 180°C (340-350°F). Then, in an oven-baking tray, spread all your fried potatoes as a bottom layer. Then, layer with the spinach mixture and cover the potatoes. Season with salt and ground black pepper. Then, pour your béchamel sauce over the spinach mixture and potatoes layers. Then, sprinkle with the cheese and red pepper flakes and bake for about 40 or 45 minutes (if your potatoes are raw, you need to 1 hour and 15 minutes baking time or until the potatoes are tender).
5- Then, let stand for 10 minutes and serve with a green salad or serve as a side dish with any meat dish.