Cook the pasta barely al dente (around 7 minutes), preheat the oven to 200° C, and grease a baking dish with 1 tablespoon of the butter.
Arrange the chicken breasts with bay leaves in a medium pot; season with 1 tablespoon of salt and add enough water to cover the chicken by 3cm. Cover the pot and bring to a boil over moderately high heat, then reduce the heat to low and simmer for about 10 minutes, until the chicken is white throughout. Take the chicken out of the pot and let cool slightly. Tear the chicken into large chunks and mix it with pasta.
Heat 2 tablespoons of olive oil in a pan. Add the onion and garlic, and cook over moderately high heat, stirring occasionally, until softened and lightly golden brown. Add the mushrooms, season with salt and pepper, and cook until browned and softened; about 5 minutes. Transfer the vegetables to the bowl with the chicken and pasta.
Use the pan again to melt 3 tablespoons of the butter over moderate heat. Add the flour, 1 teaspoon of salt, and 1/4 teaspoon of pepper and cook, stirring constantly, until a smooth paste forms; about 1 minute. Add the milk in a slow, steady stream, whisking constantly. Bring to a boil, stirring frequently, then reduce the heat to low and simmer until the sauce is thick enough to coat the back of a spoon, about 12 minutes. Remove from the heat and whisk in the sour cream and mustard. Add all cheeses and stir until melted. Scrape the cheese sauce into the bowl with the chicken and pasta, then stir in the peas.
Transfer the chicken mixture to a casserole and spread it evenly. Melt the remaining 2 tablespoons of butter and stir in the breadcrumbs and some more parmesan. Spread the butter mix over the chicken and bake for 30 to 35 minutes, until the tetrazzini is bubbling and golden brown on top. Let cool slightly before serving.
