Remove the skin from the melanzane, halve and cut into small pieces. Remove the peel from the shallots and garlic and chop finely. Peel the tomatoes, remove the seeds and cut into cubes. Cut mushrooms into small pieces.
For the garnish provencale, sauté 1 chopped shallot and 1 chopped garlic clove in a saucepan with 1 tbsp olive oil.
Add mushrooms and tomatoes, cook briefly and stir in bread crumbs. Season to taste with salt and freshly ground pepper.
Heat 2 tbsp olive oil, sauté the melanzane, a shallot and garlic in it without browning. Season with salt and cayenne pepper, pour balsamic vinegar and vegetable soup. Make 5 minutes, then in a hand mixer form, crush, pour again into the saucepan, add the whipped cream and bring to a boil again while stirring and season.
Preheat the oven to 60 degrees (fan 50 degrees, gas mark 1).
Cut the skinned monkfish into medallions, season with salt and pepper. In a frying pan with 2 tbsp olive oil, roast the medallions for 4 min on each side, remove from the frying pan and keep warm in the oven.
In the frying pan, sauté the remaining shallots with the garlic. Add rosemary and extinguish with fish stock and white wine. Boil everything by half, then thicken with cold butter and season.
Coat the fish fillets with the paste and pour the hot sauce over them. Serve with the eggplant puree.