Toast the anise seeds in a small skillet over moderate heat about 3 minutes until the anise is fragrant. Cool slightly and crush with the side of a knife.
In a food processor, combine the seeds with the cloves, saffron, paprika, and cayenne pepper. Puree with lemon juice. Transfer mixture to a shallow bowl and stir in 1/2 cup olive oil. Add the chicken thighs, turn to coat with marinade. Refrigerate 1 hour.
Meanwhile, bring water to boil in a medium saucepan. Add the salt and fava beans; cook for 1 minute; using slotted spoon, transfer fava beans to a small bowl; cool slightly. Add peas to boiling water; cook until tender, 5 to 6 minutes; drain. Peel fava beans, add to peas.
Heat remaining 2 tbsp of oil in a large Dutch oven. Remove the chicken from the marinade, shake off excess marinade. Season chicken with salt and pepper and cook over moderately high heat, turning until brown on both sides. Transfer chicken to platter.
Wipe out casserole, add butter, heat until melted. Add the mushrooms, scallions, and thyme. Cook over moderate heat, stirring occasionally, until liquid has evaporated and the mushrooms are brown, about 8 minutes. Sprinkle flour over mushrooms, cook stirring 1 minute, then slowly add beer and bring to a boil, scraping loose bits off bottom of pan.
Return chicken thighs to casserole. Cover, simmer over low heat until chicken is tender and cooked through, about 25 minutes. Add cream, fava beans, peas, and increase heat to moderate. Cook, uncovered until sauce has reduced slightly, about 5 minutes. Discard thyme sprigs. Serve chicken stew in shallow bowls, sprinkled with parsley.