Preheat the oven to 200 degrees Celsius/ 400 degrees Fahrenheit.
Chop the onion and the garlic cloves finely. Grate the carrots.
Saute: Heat the oil in a pan and saute the onions until translucent. Add the garlic and the carrots, saute for a couple of minutes more.
Cook: Add the ground beef and let it get a bit brown. Break the meat lumps with a wooden spoon while the meat is cooking. Add the tomato paste, stir well and saute for 1 more minute. Add the tomatoes, oregano, paprika, salt, and pepper to taste and bring everything to a boil. Simmer gently for 5 minutes.
Yogurt sauce:
In the meantime, mix the yogurt and the hot stock. Add ¾ cup of the grated cheese to the yogurt mixture and stir well.
Assemble the yogurt lasagna:
First layer: Place 2-3 tablespoons of the meat saucein a rectangular casserole dish of about 30x20 cm/12x8 inches, just enough sauce to thinly cover the bottom of the dish. Place lasagna sheets on top, add 1/3 of the meat sauce and 1/3 of the yogurt sauce.Repeat: lasagna sheets, 1/3 of the meat sauce, 1/3 of the yogurt sauce.Repeat: lasagna, rest meat sauce, rest yogurt sauce.Cheese: Sprinkle with the remaining 1 cup grated cheese.
Bake for about 30 minutes or until the lasagna sheets are cooked through, and the cheese is golden brown. Check by inserting a fork in the casserole; the noodles should be soft.
Rest: Let the lasagna sit for 5 to 10 minutes, cut into squares and serve with one or two of the sides suggested above.
Notes
Made from a ½ vegetable stock cube dissolved in 200 ml/ scant 1 cup hot water.
I used Gouda, but Cheddar is just as fine. Or any other kind of cheese you usually take for lasagna.