Poach the Chicken: Combine the chicken broth, bay leaves, peppercorns, salt and vegetables in a large stock pot and bring to a boil. Reduce heat to a simmer and cook for 15 minutes, carefully skimming off and discarding any foam and grease that accumulates on the surface, before adding the chicken. Add the chicken breasts whole and cook the chicken just below a boil for 15 minutes.
Move the pot to the back of the stove and cool the chicken in the poaching liquid. The chicken will finish cooking gently, leaving it moist and tender. When cool enough to handle, remove from the broth and cut into small pieces. Return chicken to the broth until needed for the casserole, straining before using. *NOTE: You can use this poaching liquid for most of the chicken stock used to make the sauce if desired.*
Preheat the oven to 375°F. Butter a 9x13-inch baking dish and set aside.
Cook the Pasta: Bring a large pot of well-salted water to a boil and cook pasta until just under al dente; length of cooking time will be determined by type of pasta you choose. Remember that the pasta will bake in the oven, so you don’t want to overcook it at this point. Drain in a colander, transfer to a large bowl, toss with 2 tsp olive oil and set aside.
Prepare the Vegetables: Meanwhile, in a large skillet, combine 2 tablespoons butter with 2 tablespoons olive oil over medium-high heat. Add the carrots, celery, and onion cooking until soft, 3 to 5 minutes, stirring occasionally. Stir in the garlic and cook for 30 seconds or until aromatic. Add the mushrooms and marjoram and cook, stirring occasionally, until the mushrooms are soft and have released their liquid, about 4 minutes. Add to the bowl with the pasta. Stir in the chopped chicken, peas, salt and pepper. Set aside.
Make the White Sauce: In a saucepan melt the butter over medium heat. Sprinkle with the flour and cook, whisking constantly, for 2 minutes until the flour no longer smells raw. Whisk in the chicken stock and cook, stirring, until smooth and thick, about 2 minutes. Whisk in the half & half and bring to just below a boil. Reduce the heat to medium and simmer, stirring regularly, until the sauce is thick enough to coat the back of a spoon, 10 to 15 minutes. Taste and add salt and pepper as needed.
Assemble Casserole: Pour sauce over chicken, pasta, and vegetables, tossing until evenly coated. Transfer mixture to the prepared baking dish and top with shredded cheese. In a small bowl toss together the Parmesan, panko, and parsley. Sprinkle seasoned breadcrumbs over the top. Bake, uncovered, until bubbly and golden brown, about 30 minutes. Serve hot.