Pat the chicken dry with paper towels and season it generously with salt, pepper, and the rosemary. Heat 2 tablespoons of olive oil over medium heat in a large Dutch oven and brown the chicken pieces in batches until nicely browned all over, about 5 to 7 minutes per batch. Transfer the browned chicken pieces to a plate and set aside.
Lower the heat to medium-low and add the garlic, saffron, fennel seeds, tomato puree, chicken stock, white wine, Pernod, 2 teaspoons salt, and 1 teaspoon pepper to the pot. Stir and scrape up any browned bits on the bottom, and simmer for 30 to 40 minutes, until the garlic is very tender, stirring occasionally.
Meanwhile, preheat the oven to 300 degrees.
Carefully pour the sauce into the bowl of a food processor fitted with the steel blade. Puree until smooth. Return the sauce to the Dutch oven and add the potatoes and browned chicken pieces with their juices. Stir carefully.
Cover the pot and bake for 45 to 55 minutes, until the potatoes are tender and the chicken is done. Check the seasonings and serve hot in shallow bowls with big dollops of rouille and slices of crusty bread.
Place the garlic and salt on a cutting board and mince together. Transfer the mixture to a food processor fitted with the steel blade. Add the egg yolk, lemon juice, saffron, and red pepper flakes. Process until smooth.
With the machine running, pour the olive oil in a thin, steady stream through the feed tube to make a thick mayonnaise emulsion. Transfer the rouille to a serving bowl and store it in the refrigerator until ready to serve.
Consumption of raw or undercooked eggs, shellfish and meat may increase the risk of foodborne illness.
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