Heat the oven and butter the dish: Heat the oven to 350°F and grease a 9x13 baking dish. Put the dried bread cubes in your largest mixing bowl.
Brown the sausage: Cook the sausage in a large skillet over medium heat for 8-10 minutes, breaking it into small pieces, until no pink remains and it reaches 160°F. Lift it out with a slotted spoon into the bowl with the bread and leave the drippings behind in the skillet.
Cook the onion and celery: Add the butter to the skillet with the drippings. Once it melts, add the onion and celery and cook for 7-8 minutes, until soft and translucent with no crunch left. Stir in the garlic and cook 1 minute more.
Combine: Scrape the vegetables and every bit of butter from the skillet into the bowl. Add the sage, rosemary, parsley, salt and pepper and toss until the sausage and vegetables are spread evenly through the bread.
Add the broth and eggs: Whisk the chicken broth and beaten eggs together, pour the mixture over the bread, and fold gently until every cube looks damp. Let the bowl sit 5 minutes so the bread pulls the liquid all the way to its center, then fold once more.
Bake uncovered: Spread the stuffing in the buttered dish without packing it down. Bake uncovered for 55-65 minutes, until the top is deeply golden and crisp and the center reads 165°F on a thermometer. Tent it loosely with foil if the top browns before the center is hot.
Notes
The bread must be dried before it goes in the bowl, or it turns to paste instead of absorbing the broth. Cook the pork sausage to an internal temperature of 160°F while browning, and bake the stuffing uncovered until the center reads 165°F, which is the USDA's minimum for any stuffing. Let the soaked bread mixture rest 5 minutes before it goes in the pan.