Season and sear the fish: Rub the fish chunks with 1 tbsp of the olive oil, a pinch of saffron, 1 tsp of the salt, the black pepper and the cayenne. Heat a large Dutch oven or heavy pot over medium-high heat with another tablespoon of oil and sear the fish skin-side down in a single layer until deeply golden, about 2 minutes per side. Remove to a plate — it will finish cooking later.
Build the aromatic base: In the same pot, add the remaining tablespoon of oil, the fennel, carrots, celery and the whole star anise. Cook for 4 minutes, scraping up the browned bits from the fish. Add the crushed garlic, sliced shallots and a pinch of cayenne, and cook 2 more minutes until the shallots soften.
Flambe with Pernod: Return the fish to the pot. Pour in the Pernod and let it bubble hard for about 30 seconds, tilting the pot so the alcohol burns off and lifts all the caramelized flavor off the bottom. Do not skip this — it is where the sharp anise punch comes from.
Simmer it down: Pour in the white wine, fish stock, diced potatoes, canned tomatoes, basil and parsley. Bring to a boil, then reduce to a steady simmer and cook uncovered for 20 minutes, until the potatoes are completely tender and the fish flakes easily.
Blend it silky: Fish out and discard the star anise. Blend the soup with an immersion blender until completely smooth and thick — the potatoes and fish break down into the broth and give it its body. Taste and season with the remaining 1/2 tsp salt and more cayenne or lemon if needed.
Make the rouille: While the soup simmers, grind the saffron to a powder with a mortar and pestle, add the boiling water and let it steep 5 minutes. Whisk the egg yolks with the garlic and Dijon in a bowl, then pour in the two oils in a slow, thin stream, whisking constantly, until thick and glossy. Stir in the saffron water, lemon juice and salt.
Serve it proud: Ladle the hot soup into warm bowls. Drop a generous spoonful of rouille on top of each, scatter with extra basil, and serve immediately with the griddled toast for dragging through the rouille.