Preheat the oven to 350 degrees F.
Place a large pot over medium-low heat. Add the leftover potatoes and hot water and stir with a wooden spoon until the potatoes begin to soften and get hot, 3 to 5 minutes. Add the milk, butter, yogurt, 1 teaspoon ajwain and a pinch of salt and stir well until the mixture is smooth. Set aside.
Place a large skillet over medium heat and add the oil. When it is hot, add the garlic, ginger and onions, and cook until the onions are soft and translucent, about 3 minutes. Add the celery and stir, and then add the garam masala, Italian mixed herbs, the remaining 1 teaspoon ajwain seeds and a pinch of salt, and cook for about 30 seconds. Stir in the ground beef, stir and let it cook through, about 5 minutes. Add the crushed tomatoes and 1/2 cup water, and then stir in the cooked lentils and simmer for 5 minutes. Pour into a 9 by 13-inch baking dish and sprinkle with the mozzarella. Spread the mashed potatoes evenly over the top and sprinkle with the paprika. Bake until it is bubbling and hot, about 30 minutes.