For the Sausage - Heat a large skillet on medium heat and add the sausage. Using a heat proof spatula, break up the sausage as its cooking so that the pieces are all about the same size.
Stir the sausage as it cooks. The heat may need to be turned down slightly so that the sausage doesn't turn too brown before its completely cooked through.
Continue to stir as the sausage cooks until the sausage is thoroughly cooked (about 15 minutes).
After the sausage is done cooking, turn the heat off and transfer the sausage onto a paper towel-lined plate to drain off any excess grease. Set aside.
Reheat the same pan that the sausage was cooked in on medium heat and add olive oil.
For the Celery and Onion - To the pan, add the celery, onions and a couple dashes of pepper. Sauté the celery and onions until they start to turn translucent (about 8 minutes).
Combining the Cooked Sausage, Celery and Onion - Turn off the heat, and put the sausage back in the skillet and stir all of the ingredients together.
If Making This Recipe Ahead of Time - This is the point where you can stop if making the dish ahead of time. Add the celery, onions, and sausage to a bowl, cover it, and store in the refrigerator until you’re ready to make the stuffing.
About 15 minutes before you’re ready to serve the stuffing; to a medium to large size pot, add butter and 1 cup of broth (reserving 1/2 cup).
Heat the pan on low to medium heat until the butter melts. Then stir in the sausage, onion, and celery mixture. Then add the stuffing mix and stir together.
Turn off the heat and cover the pan. Let the stuffing sit with the lid on for about 8 minutes.
Then check the consistency of the stuffing and if it’s not moist enough for your liking, add some or all of the remaining 1/2 cup broth.
Stir the stuffing and serve warm.