Preheat the oven to 350 degrees.
Spray a lasagna pan with Pam.
Sprinkle the chicken with salt and pepper. Add chicken to a baking dish and bake covered with foil for 40 minutes or until juices run clear. Once cooled, coarsely shred the chicken into bite-size pieces and place in a large bowl. Turn up heat on oven to 400 degrees.
Melt 1 tablespoon butter and 1 tablespoon olive oil in a large deep nonstick frying pan over medium-high heat. Add the mushrooms and saute over medium heat until the liquid from the mushrooms evaporates and the mushrooms become pale golden, about 12 minutes. Add the onion and thyme, and saute until the onion is translucent, about 5 minutes. Add garlic and stir until fragrant. Lightly salt and pepper and transfer the mushroom mixture to the bowl with the shredded chicken.
Melt 3 more tablespoons butter in the same pan over medium-low heat. Add the flour and whisk for 2 minutes. Whisk in the milk, cream, nutmeg, and lightly salt and pepper. Increase the heat to medium. Bring to a boil. Simmer, until the sauce thickens slightly, whisking often, about 10 minutes. Set aside.
In a large Dutch oven bring salted water to a boil. Add the linguine and cook until it is tender but still firm to the bite, stirring occasionally, about 9 minutes. Before draining, with a measuring cup, dip out 1 cup of the hot pasta water. Drain pasta. Return pasta to the Dutch oven. Add sauce, mushroom and chicken mixtures, peas and sliced olives. Stir gently until well mixed. Add the pasta water a little at a time until you have a soupy consistency. Pour the pasta mixture into the prepared lasagna pan.
Stir the cheese and breadcrumbs in a small bowl to blend. Sprinkle the cheese mixture over the pasta. Dot with the remaining 3 tablespoons of butter. Bake, uncovered, until golden brown on top and the sauce bubbles, about 25 minutes.