Spread the bread cubes on 2 baking sheets and bake at 300°F (150°C) for 20 to 25 minutes, stirring once, until dry. Or leave them out uncovered overnight.
Melt the butter in a large skillet over medium heat. Cook the onion and celery for 8 to 10 minutes until soft. Add the garlic, sage and thyme and cook 1 minute more.
Heat the oven to 350°F (175°C) and butter a 9x13-inch baking dish.
In a very large bowl, toss the bread with the vegetables and butter, parsley, salt and pepper.
Whisk the eggs with 2 1/2 cups broth, pour over the bread and fold gently until evenly moist. Add up to 1/2 cup more broth if there are dry spots.
Spread in the dish, cover with foil and bake for 30 minutes.
Uncover and bake 15 to 20 minutes more, until golden and crisp on top and the center reaches 165°F (74°C).
Rest for 5 minutes, then serve warm.
