Melt butter in a pan over medium heat.
Sprinkle in the flour and whisk to form a roux.
Cook the roux for 2-3 minutes until it starts to brown.
In a separate saucepan, bring the shrimp stock to a boil.
Remove from heat and let it cool slightly.
Slowly add the warmed shrimp stock to the roux while whisking constantly.
Ensure the mix is smooth without any lumps.
Add the sherry wine, Worcestershire sauce, and cayenne pepper to the mixture.
Continue to whisk until well blended.
Gradually add the grated cheese in small pieces.
Whisk continuously to melt and integrate the cheese until the sauce is smooth.
Add the chicken base and blend thoroughly.
Let the sauce simmer for a few minutes to thicken to your desired consistency.