Tear your sourdough bread into chunks and spread it out on a sheet pan. Place it in a warm oven until dried out, about 1 hour on low heat.
Increase the oven temperature to 325°F.
In a medium saucepan, melt 3 tablespoons of butter over medium heat. Add the onion and celery, sautéing until they’re tender and translucent, about 6 to 8 minutes.
Stir in the garlic and flour, cooking and whisking constantly until fragrant (about 1 minute). Add garlic salt, salt, and pepper, then gradually pour in the cream. Continue to cook, whisking often, until it just begins to simmer, around 5 minutes.
Spread the chicken evenly in a 9x13-inch baking dish, then layer the sour cream on top. Pour the cream sauce evenly over the chicken and sprinkle the dried sourdough bread pieces on top.
Melt the remaining 4 tablespoons of butter, mix in the chicken broth, and pour it over the casserole, making sure to coat the bread well.
Bake, uncovered, until the casserole is bubbling, about 30 minutes. For a golden, crispy top, broil for the last 3 to 4 minutes.