Melt the butter in a medium saucepan over medium heat.
Add the flour to the melted butter and whisk to form a roux.
Cook the roux for about 2-3 minutes until it turns light golden brown.
Gradually add the broth while whisking to prevent lumps.
Bring the mixture to a gentle boil, stirring frequently.
Stir in the Worcestershire sauce.
Season with salt and pepper to taste.
Add a splash of cream if desired for richness.
Reduce heat and let simmer for 5-7 minutes until thickened.
Strain through a fine-mesh sieve for a smoother consistency if preferred.