Preheat the oven to 450 degrees F.
Cook the linguine noodles according to package directions.
While the noodles are cooking, shred about 1 ½ cups of a rotisserie chicken and add to a large mixing bowl.
Drain the noodles and add to the mixing bowl with the chicken.
In a large skillet, melt 1 tablespoon of butter and add the mushrooms. Sauté the mushrooms for about five minutes, then add in the minced garlic. Cook for another 3-5 minutes or until the mushrooms are soft and tender. Transfer to the bowl with the chicken and noodles.
In the same skillet, melt 2 ½ tablespoons of butter over medium-high heat. Add in the flour, salt, and pepper, and whisk to combine. Bring to a simmer, stirring constantly. Let simmer for about 1-2 minutes then add in the chicken broth. Gradually add in the milk while continuously stirring. Bring to a simmer and let cook until the sauce thickens, stirring frequently.
Once the sauce has thickened, pour over the chicken and noodles in the mixing bowl. Add 3 tablespoons of the freshly grated parmesan cheese and stir to combine.
Grease two individual Au Gratin-style dishes or large 13 x 9 casserole dish if doubling the recipe. Transfer the chicken tetrazzini mixture to the baking dishes.
In a small dish, combine the bread crumbs and 3 tablespoons of the freshly grated parmesan cheese. Sprinkle over the top of each dish.
Place the dishes into the oven and bake for 10 to 15 minutes or until bubbly and topping is golden brown. Remove from oven and serve.