In a large saucepan, melt the unsalted butter over medium heat.
Add the finely chopped onion and cook for 4-5 minutes until softened and translucent.
Add the minced garlic and cook for an additional 1 minute, stirring frequently to avoid burning.
Sprinkle the all-purpose flour over the onion and garlic mixture and stir constantly for 2-3 minutes to cook the flour and form a roux.
Gradually whisk in the beef broth and chicken broth, ensuring there are no lumps.
Add the Worcestershire sauce, dried thyme, black pepper, salt, and soy sauce to the saucepan.
Bring the mixture to a gentle boil, then reduce the heat to low and simmer for 20-25 minutes, stirring occasionally, until the gravy thickens to your desired consistency.
Taste and adjust seasoning with additional salt or pepper if needed.
Remove from heat and serve warm over mashed potatoes, rice, or your favorite roasted meats.