Add flour, pepper, cayenne and thyme, whisk constantly for 1-2 minutes.
Gradually add whipping cream and chicken broth stirring so not to clump gravy.
Add sausage and continue to stir until gravy is at desired consistency.
Notes
Preventing Clumps. The trick to a creamy texture is to slowly add the liquids to your roux while whisking the entire time.
Adjust the Consistency. For a thicker consistency, increase the flour by 1-2 tablespoons. For a thinner gravy, simply add more broth to the skillet.
Drain the Grease. Be sure to drain off the extra grease from the sausage to prevent the gravy from ending up overly greasy.
Make Ahead. This tastes even better the next day. Cook the gravy the night before, let it cool, and store in the refrigerator. Reheat in your cast iron skillet over medium heat and adjust the consistency before serving.