Wash and trim the green beans. Fill a stockpot about ⅔ full of water and bring to a boil over medium heat. Add 2 tablespoons of the kosher salt and the concentrated chicken base, stirring to dissolve.
Add the green beans and boil for 10 minutes. Drain the beans and place them in a bowl of ice water to stop them from cooking further. Spread them out onto a towel to dry while you make the sauce.
Melt 3 tablespoons of the butter in the stockpot, over medium heat. Toss in the chopped shallot and sauté until tender and transparent, about 7 to 10 minutes.
Add the chopped mushrooms and continue cooking until the mushrooms are very tender, about 10 to 12 minutes.
Stir in the remaining teaspoon of kosher salt, the black pepper, and the remaining tablespoon of butter. Toss in the flour and cook for an additional 3 minutes, stirring frequently.
Pour in the chicken stock and cook until slightly thickened, about 6 to 8 minutes.
Add the half and half along with the cream and the Parmesan cheese. Cook, stirring frequently until the sauce is thick, about 5 to 7 minutes.
Place the green beans back in the pan and toss to coat. Transfer the beans with the sauce to a large baking dish that has been sprayed with a cooking spray.
Bake in a 375-degree oven for 30 minutes. Let the dish rest for about 5 minutes and top with the fried onions.