Peel the carrots and finely grate, peel the onion and cut into small cubes. Blanch the tomato: make a cut in the skin, then pour boiling water over it and then place in ice water. The tomato skin should come off easily. Cut the tomatoes into small cubes. Finely grate the cheese and heat the milk. Preheat the oven to 180°C.
Prepare the filling: fry the onions and carrots in hot oil, add the minced meat to the vegetables and fry it for 5 minutes, stirring constantly. Add tomato cubes, add salt and simmer for another 10 minutes.
Prepare the sauce: add flour to melted butter in a frying pan, stirring continuously with a spatula. Then pour in the heated milk and continue cooking, stirring constantly, until the sauce thickens. Remove it from the heat and cool slightly.
Assemble the lasagna: Grease a lasagna pan with butter, pour a little sauce on the bottom, place the first sheet and brush it with sauce. Place a portion of the meat filling on the sheet and sprinkle with grated cheese. Repeat procedure with remaining lasagna sheets, sauce, meat filling and cheese.
Sprinkle the top layer generously with cheese, cover the pan with a lid or foil and place in an oven preheated to 180°C for 20 minutes.
Remove the lid or foil and bake for another 10 minutes until golden brown.
Cut into portions and serve.