Prepare the linguine according to package directions. Drain. Set aside.
Melt 2 tablespoons of butter in a deep large, oven-safe, skillet over medium-high heat. Add the mushrooms to the skillet, and sauté over medium-high heat until the liquid from the mushrooms evaporates about 1-2 minutes.
Add the onion and bell pepper and cook until they are soft, about 7 minutes. Add the garlic and sauté about 1 minute. Pour in the Sherry and let it cook until the Sherry evaporates. Transfer the vegetable mixture to the bowl with the cooked, shredded chicken. Set aside.
Combine asiago and parmesan cheese together in a bowl. Set aside.
Melt 3 more tablespoons butter in the same pan over medium-low heat. Add the flour and whisk for 2 minutes. Whisk in the Half and Half, salt, and pepper. Increase the heat to medium. Simmer, uncovered, until the sauce thickens slightly, whisking often, about 5 minutes. Remove from heat and stir in greek yogurt and half of the shredded asiago and parmesan cheese.
Add the cooked chicken, vegetables, and linguine to the chicken mixture. Toss until the sauce coats the pasta and the mixture is well blended.
Preheat the oven to 425 degrees F.
Stir the remaining asiago and parmesan cheese and breadcrumbs in a small bowl to blend.
If you don't have an oven-safe skillet, transfer the chicken tetrazzini into prepared baking dish.
Sprinkle the cheese and bread crumb 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. Serve the Chicken Tetrazzini with Asiago Cream sauce while it is still hot.