In a medium saucepan or skillet over medium heat, melt 2 tablespoons of unsalted butter. Add the finely diced yellow onion and cook until softened and translucent, about 5-7 minutes. Add the minced garlic and cook for another minute until fragrant.

Sprinkle the 2 tablespoons of all-purpose flour over the cooked onions and garlic. Whisk continuously for 1-2 minutes until a light golden roux forms. This step is crucial for cooking out the raw flour taste.

Gradually whisk in the 2 cups of beef broth, a little at a time, ensuring no lumps form. Bring the mixture to a simmer, whisking frequently, until the gravy begins to thicken to your desired consistency, about 5-8 minutes.

Stir in the 1 tablespoon of Worcestershire sauce and 1/2 teaspoon of dried thyme. If using, add 1/4 teaspoon of browning sauce for a richer color. Season with salt and freshly ground black pepper to taste. Keep the gravy warm over low heat, stirring occasionally.

Add the thinly sliced roast beef directly into the simmering gravy. Gently toss or stir the beef to coat it evenly and allow it to heat through completely, which should take about 3-5 minutes. Be careful not to overcook, or the beef may become tough.

While the beef is heating, prepare the bread. Toast the 8 slices of sturdy white bread or Texas toast. You can toast them in a toaster, under the broiler, or in a pan with softened butter until golden brown.

For each serving, place two slices of toasted bread on a plate. Pile a generous amount of the hot, gravy-covered roast beef onto one slice of bread.

Ladle a generous amount of the rich brown gravy over the beef and the top slice of bread, ensuring the bread is thoroughly drenched. Serve immediately, traditionally with a side of creamy mashed potatoes to soak up extra gravy.