HEAT oil in a deep 10-in. oven-safe frying pan over medium-high. Add onion and cook until almost soft, 3 min. Add sausages and cook until browned, 3 to 4 min. Add mushrooms, garlic and pepper flakes and cook until mushrooms are soft, 5 min. Stir in tomatoes and reduce heat to medium. Gently boil until sauce thickens slightly, 12 to 15 min. Transfer to a large bowl.
STIR egg, ricotta and 1/2 cup of the parmesan in a medium bowl.
SPREAD 1 heaping cup of the meat mixture in bottom of same frying pan. Cover with 2 lasagna noodles, cutting to fit pan. Layer with 1 heaping cup of meat mixture and half of the ricotta mixture. Repeat layers, ending with meat mixture.
BRING to a boil, then reduce heat to medium-low. Cover and simmer until noodles are cooked through, 12 to 15 min. Remove from heat. Sprinkle with remaining 1 cup parmesan and mozzarella.
BROIL in centre of oven until cheese is melted and browned, 1 to 2 min.