How to Make It
Heat oven to 375° F. Heat the oil in a large skillet over medium-high heat. Cook the sausage until browned, turning occasionally, 3 to 5 minutes. Transfer to a plate and reserve the skillet.
Butter a 9-by-13-inch baking dish. Divide the bread between 2 rimmed baking sheets and bake until dry and crisp, 10 to 12 minutes.
Meanwhile, wipe out the skillet and melt the butter over medium heat. Add the onions, celery, bell peppers, 1 teaspoon salt, and ¼ teaspoon black pepper. Cook, stirring occasionally, until very tender and beginning to brown, 10 to 12 minutes. Add the wine and cook until evaporated, 2 to 4 minutes; transfer to a large bowl and let cool for 10 minutes.
Add the bread, broth, eggs, sausage, oregano, and ½ teaspoon salt to the vegetables and toss to combine. Transfer to the prepared baking dish. Cover with buttered foil and bake for 20 minutes. Uncover and bake until browned, 20 to 30 minutes more.