1. For the aioli: peel the garlic cloves and put them in the mortar with a pinch of salt. Crush them into a puree, add the egg yolk and lemon juice and mix with the pestle to obtain a homogeneous mixture. Slowly incorporate the oil in a thin stream, stirring or whisking until a creamy mayonnaise is formed. Incorporate the mustard.
2. Peel the onion and dice all the vegetables into small cubes. Peel the potatoes and cut them into slices. Take the zest from the orange.
3. Heat a drizzle of oil in a saucepan and sauté the small diced onion, fennel, leek, and carrot. Add the orange zest and continue cooking for 10 minutes over medium heat, stirring.
4. Increase the heat. Pour in the wine and broth, add the saffron and potato slices, and cook for 12 minutes. Season with Espelette pepper and salt.
5. Reduce the heat and cook the fish pieces in the mixture. Gently remove them from the saucepan and keep warm.
6. Remove the saucepan from the heat and incorporate the aioli into the soup. Return to low heat and stir for 3 minutes, until the mixture is smooth and creamy. Be careful not to let it boil!
7. Serve with grilled baguette rubbed with garlic and a jar of rouille.