Slice the onion, celery and carrots, and smash and mince the garlic.
Whisk the olive oil, capers and mustard, then mix with the chopped mushrooms.
Mix the Arugula, tomatoes and balsamic.
This dish works best in a terra cotta pan that will hold all the fish in a single layer.
Fire the oven until the carbon burns off (650F+), then push the fire to one site and let the oven rest for a few minutes. Shovel out any excess coals. You want a hot oven, which is capable of browning your vegetables from the dome heat, but not so hot that you burn everything in the first few minutes.
Place the onion, carrot, celery, garlic and olive oil in the pan, and bake for 3-5 minutes, or until the onions and garlic are translucent and lightly brown.
Assemble the fish over the vegetables, and top with the mushrooms and mustard sauce. Return the pan to the oven to bake.
When the mushrooms are brown, and the fish is baked, remove the pan from the oven, and top with the Arugula and balsamic. Place the cooking pan on the table — take care to place all four layers on every plate when serving.