Fry the beef. Heat a frying pan, pour in the oil and heat it up. Add the beef and fry, stirring, over high heat until golden brown. Reduce the heat to medium and add the chopped onion. Fry until the onion is translucent.
Fry the vegetables. Add the carrots, eggplant, and bell pepper to the pan with the beef. Simmer for 5 minutes. Add the tomatoes and stir. Pour in enough water to cover all the ingredients in the pan. Add the spices: pepper, paprika, coriander, cumin, and star anise. Simmer the dish over medium heat for about 10 minutes, stirring occasionally. Then add the potatoes. Simmer for 5-8 minutes until the potatoes soften. Turn off the heat and let the lagman sit.
Place the prepared noodles in a plate and pour over the meat and vegetables.