In a food processor, combine the basil leaves, garlic and pine nuts. Slowly add the oil scraping down the sides a couple of times. Add Parmesan and season, to taste. Process briefly until combined. Add the eggs, egg yolk, and brioche crumbs. Mix for 1 minute and set aside. Arrange the fillets on a baking pan, pat dry, and season with salt and pepper. Place the crust mixture on a sheet of parchment paper; level off to 1/4-inch thick. Cut the parchment and the crust, using a sharp knife, to fit the size of each fillet, and gently slide butter on top of each fillet using a warmed spatula. Bake for 15 minutes.
For the portobello mushrooms:
Preheat grill on high.
Mix all ingredients and rub marinade over portobello caps. Cook on grill for about 5 minutes on both sides until both sides are charred. Once charred, remove from grill and transfer into a roasting pan. Roast in the oven for 10 minutes. Remove pan from the oven and keep warm.
For the beurre blanc:
Combine the shallots, peppercorns, wine, lemon juice and vinegar in a medium saucepan over medium heat. Simmer for 7 minutes until the sauce liquids have reduced by two-thirds. Add the cream and simmer for 10 minutes. Do not boil. Remove from heat and whisk in the butter a little at the time. Strain through a fine mesh strainer. Adjust seasoning with salt and pepper, and stir in the sun-dried tomato paste. Hold the sauce in a bain-marie or canister to keep warm until ready to serve.
For the creamed fennel:
Heat large saute pan over medium heat. Add butter and melt, but be careful not to burn the butter. Once melted add the blanched fennel and saute over low heat. Season, to taste, with salt and pepper. Add heavy cream and reduce by half. Do not boil.
To serve, arrange the creamed fennel in the center of each plate, top with the portobello mushrooms and the fish. Garnish with the broccoli and finish with the beurre blanc.