Into a large roasting pan, stir together cubed stuffing mix, sausage, diced celery, and diced onion.
In a saucepan over medium heat, bring milk to a low simmer. Once heated, pour over stuffing mix, sausage, celery, and onion. Salt and pepper to taste.
Add in beaten eggs and stir to combine.
Top dressing with 4 tablespoons of butter before placing roasting pan into oven heated to 325 degrees F.
Bake dressing for 2-3 hours, stirring every 30 minutes. At which time, continue adding more butter and chicken broth, until the dressing reaches your desired consistency.
Notes: After baking, the dressing can be cooled and placed into a storage container in the refrigerator. When ready to reheat, place mixture into a slow cooker and heat over low, stirring occasionally. If mixture becomes too dry add more chicken broth.
*Substitute the sausage for cooked ground beef. Or do a 50/50 combination of sausage and ground beef.