In a 2-quart pot, bring chicken broth to a boil. Add mushrooms and onions and bring back to a simmer. Reduce heat to a slow simmer and cover for at least 1 hour.
In a separate large pot, melt the butter, then add the flour. Whisk until evenly incorporated. Continue to whisk while slowly adding half-and-half to the roux. Add bay leaf and stir constantly until the sauce is thickened and smooth. Remove the bay leaf and discard.
Add the mushroom broth to the roux and stir until evenly incorporated. Season with salt, pepper and hot sauce, to taste. Serve immediately.
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