To make the sauce: Heat olive oil in a large non-reactive saucepan over high heat. Add the garlic clove, bay leaf, peppers, tomatoes, and water and bring to a boil. Lower the heat to medium and simmer until the peppers are tender, about 25 minutes. Add the oregano halfway through cooking. Transfer the mixture to a blender or food processor and puree until smooth. Season the puree with salt and pepper and return it to the pan to keep warm. You should have about 11/2 cups. The sauce can be covered and refrigerated for 1 to 2 days.
To make the stuffing: Drop the garlic, oregano, olives, and 1 tablespoon of the olive oil into a food processor and process until very finely chopped. Season with salt and pepper, pulse again, and scrape into a small bowl. The stuffing mixture can be made ahead to this point and refrigerated for several days.
Preheat the oven to 400 degrees F.
Season the inside of the thighs with salt and pepper. Put about 1 1/2 teaspoons of the olive paste inside each thigh. Tie closed with kitchen string and season with salt and pepper. Season the chicken legs with salt and pepper.
Heat 2 tablespoons of the olive oil in a large ovenproof skillet over medium-high heat until hot. Lower the heat to medium, add the chicken thighs and legs skin side down and saute until lightly brown all over. Put the skillet in the oven until the chicken is opaque throughout, about 20 minutes. Transfer to a plate and keep warm.
Pour off the fat from the pan, add the water, place over medium heat, and stir and scrape up all the browned bits from the bottom and sides of the pan. Simmer until slightly reduced. Add 1 cup of the sauce and reheat gently. Add any juices from around the chicken.
Meanwhile, bring a large pot of water to a boil and add salt. Add the pasta and cook until al dente, about 12 minutes. Drain and return to the pasta pot. Add the remaining sauce and toss well to coat.
Divide the fettuccine among 4 plates. Slice the thighs and arrange slices and 1 leg next to the fettuccine. Sprinkle with parsley and grated Parmesan. Serve immediately.