In a saute pan or saucepan over medium heat, melt butter.
Add flour and whisk to make a paste (continue whisking until no lumps remain). Cook for one minute.
Slowly add broth to pan, whisking continuously. Add Cajun seasoning and pepper, whisking to incorporate. Cook for 5-7 minutes or until desired thickness is achieved, while whisking continuously.
Remove pan from heat and add hot sauce, stirring to incorporate. Taste test and add more hot sauce to taste. Last, add salt as needed and stir to incorporate (season to taste).