Heat the olive oil in a large skillet over medium heat. Add the onion and garlic and sauté until the onion is softened, about 5 minutes. Stir in the mushrooms and cook until tender, about 5 minutes more. Add the tarragon, oregano, thyme, and pepper and cook for 1 minute more.
Stir in the flour and cook for 1 minute. Gradually stir in the chicken broth and bring the mixture to a boil. Reduce the heat and simmer until thickened, about 5 minutes. Remove from the heat and stir in the sour cream.
Add the chicken to the sauce and mix well. Pour the mixture into a 9x13 inch baking dish. Sprinkle the cheese and bread crumbs on top. Bake for 20 minutes, or until the cheese is melted and the casserole is heated through.
Interesting Facts
Tarragon is a fragrant herb with a slightly sweet, anise-like flavor.
This casserole can be made ahead of time and refrigerated until ready to bake.