Separate broccoli into small florets. Place in a microwave-safe container with 1 tbsp water, cover loosely with plastic wrap, and microwave at 600W for 1 minute. Trim the base of shimeji mushrooms and separate them.

Pat the cod fillets dry with paper towels, cut into thirds, and season with salt and pepper.

Heat olive oil in a frying pan over medium heat. Add the cod and cook until both sides are golden brown. Remove from the pan.

Wipe the pan clean, add butter, and heat until melted. Add broccoli and shimeji mushrooms, sauté until mushrooms soften. Sprinkle flour and stir until no longer powdery. Add milk, consomme, salt, and pepper, stirring to thicken.