Melt butter in a saucepan over medium low heat and sprinkle in flour. Whisk together to form a roux and continue whisking for 4 minutes, or until the roux begins to turn golden brown.
Add cajun seasonings to the roux, stir to combine, then add the chicken broth, hot sauce, and Worcestershire sauce in small splashes at a time, ensuring the liquid fully incorporates before adding more.
Once all liquid has been added, bring the gravy to a simmer for approximately 2 minutes, or until it reaches your desired consistency. Then serve immediately.
Notes
If your gravy is too thin, just simmer it longer. It thickens as it cooks. If it gets too thick, it can be thinned out with a couple dribbles of water.