Food Network teaches how to crush, slice and mince garlic. Peel off some of the papery skin from the garlic and then smash the head of garlic with the heel of your hand to loosen the cloves; if you only need a few cloves, leave the head intact and pull some off. Separate the cloves. To peel a clove, cut away the root end with your knife. Lay the flat side of the knife over the clove while holding the knife handle, then with the heel of your free hand carefully whack the knife against the garlic to separate the skin from the clove. To crush the peeled garlic, lay the flat side of the knife over the clove and smash it again. To slice peeled garlic, lay the clove flat on the cutting board and hold it with the fingertips of one hand, keeping them curled under. Using a rocking motion with the knife, make thin slices by moving the knife slowly across the clove. To mince peeled garlic, lay the flat side of a knife over the clove and smash it. Roughly chop the clove then move your free hand flat across the tip of the knife and use a rocking motion to chop the garlic until it’s finely minced.
Spread 1 tablespoon of butter over a 13 by 9 by 2-inch baking dish. Melt 1 tablespoon each of butter and oil in a deep large nonstick frying pan over medium-high heat. Sprinkle the chicken with 1/2 teaspoon each of salt and pepper. Add the chicken to the hot pan and cook until pale golden and just cooked through, about 4 minutes per side. Transfer the chicken to a plate to cool slightly. Coarsely shred the chicken into bite-size pieces and into a large bowl.
Meanwhile, add 1 tablespoon each of butter and oil to the same pan. Add the mushrooms and saute over medium-high heat until the liquid from the mushrooms evaporates and the mushrooms become pale golden, about 12 minutes. Add the onion, garlic, and thyme, and saute until the onion is translucent, about 8 minutes. Add the wine and simmer until it evaporates, about 2 minutes. Transfer the mushroom mixture to the bowl with the 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, broth, nutmeg, remaining 1 3/4 teaspoons salt, and remaining 3/4 teaspoon pepper. Increase the heat to high. Cover and bring to a boil. Simmer, uncovered, until the sauce thickens slightly, whisking often, about 10 minutes.
Bring a large pot of 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. Drain. Add the linguine, sauce, peas, and parsley to the chicken mixture. Toss until the sauce coats the pasta and the mixture is well blended.
Transfer the pasta mixture to the prepared baking dish. 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.