To make the rouille, mash the roasted pepper, parsley, egg yolk, garlic, lemon juice, and salt with a potato masher in a small bowl, or pulse everything in a food processor. Slowly whisk in the oil, barely dribbling it in at the beginning and then building to a slow, steady stream. If the sauce is too thick, add a little of the bouillabaisse broth once it’s made.
To make the bouillabaisse, heat the oil in a medium saucepan over medium-high heat. Add the carrot, fennel, leeks, onion, salt, and red pepper flakes and sauté for 10 minutes, or until the onions are translucent and the rest of the vegetables are soft. Add the garlic and sauté for 1 minute. Then add the stock, wine, and saffron and bring to a boil. Add the mussels and Pernod, cover, and boil for 2–3 minutes. The mussels are done when they open completely. Remove any that don’t open at all. Serve immediately, with rouille and a baguette for dunking.