Preheat oven to 175 degrees C. Grease a biggish baking dish.
Bring a large pot of lightly salted water to a boil. Add pasta and cook for 8 to 10 minutes or until al dente; drain.
In a large pan, brown the mince
Remove the mince to a separate bowl and saute garlic and onion in the same pan.
After garlic and onion has softened add grated carrot, beans, tomatoes, tomato concentrate. Cook for another 5 mins, add the cooked mince, then remove from heat
In a bowl, combine cheddar, parmesan, and most of mozarella and beaten egg. Stir until well combined.
In the prepared baking dish layer half the pasta, half the sauce and half the cheese mixture. Repeat. Top with remaining mozzarella.
Bake in preheated oven 34 to 40 minutes, until hot and bubbly.