Melt the butter in a large saucepan over medium-high heat. Cook and stir the mushrooms, onion and garlic in the butter until tender. Reserving the liquid in the saucepan, remove the mushroom mixture to a bowl. Return the butter mixture to medium-high heat.
Whisk together the flour and half-and-half until smooth; set aside.
Season the beef with salt and pepper; cook the beef in the reserved liquid until browned, about 5 minutes. Stir the wine, beef bouillon, thyme, basil, oregano, bay leaves, and pepper; reduce heat to medium-low and simmer 10 minutes. Slowly stir in the flour mixture and simmer, stirring occasionally, until the sauce thickens, 20 to 30 minutes. Add the mushroom mixture and stir.
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