Preheat the oven to 375°F. Grease a 2-quart rectangular baking dish with the butter.
Heat the oil in a large heavy skillet over medium heat. Add the sausage and cook, stirring for 3 minutes. Add the onions, celery, salt, and black pepper. Cook, stirring until the vegetables are soft, 2 to 3 minutes.
Add the garlic and cook until fragrant, about 30 seconds. Remove from the heat and let cool.
Combine the eggs, cream, and milk in a large mixing bowl and whisk to blend well. Fold in the sausage mixture, cheese, and green onions. Add the bread cubes, pushing them into the sausage mixture.
Pour into the prepared baking dish. Bake until the top is golden brown, about 45 minutes. Remove from the oven and let rest for 5 minutes before serving.