Preheat the oven to 350 degrees F (convection) and lightly grease a 9x13 baking dish.
Cut the bread into ½ inch cubes (it ends up being around 12 cups total) and spread evenly across 2 large baking sheets. Transfer to the oven and bake until completely dry and it is beginning to crisp, about 20 minutes. Remove from the oven and set aside.
Meanwhile, heat a large skillet over medium heat and melt 9 tablespoons of the butter. Add the onion, celery, garlic, thyme, 1 tsp salt and ½ tsp pepper. Cook, stirring often, until the onions and celery are very tender, 8 to 10 minutes. Transfer to a large mixing bowl and set aside.
Increase the heat in the same skillet to medium-high and add the italian sausage and sage. Cook, breaking up the meat with a wooden spoon, until the sausage is cooked through, about 6 minutes.
To the sausage, add the remaining 1 tablespoon of butter and toss until coated. Add the wine, stir to combine, and reduce by half, about 2-3 minutes. Add to the large mixing bowl with the onions and celery.
Add the toasted bread to the mixing bowl and toss until well combined. Add the parsley, dried sage, dried thyme, whisked eggs, chicken broth and the remaining 1 tsp salt and ½ tsp pepper and toss again to combine.
Pour into the prepared baking dish and bake, uncovered, for about 20-25 minutes, until the bread is browned.