Preheat the oven to 350°F. Spread the cubed sourdough on a baking sheet. Drizzle with olive oil, season lightly with salt and pepper, and bake for 20 minutes, until lightly toasted. Set aside. Increase oven heat to 375°F.
In a large skillet over medium heat, melt the butter. Add the onion and celery and sauté for 3 minutes, until softened. Stir in the broth and bring to a boil. Reduce heat and simmer for 10 minutes.
In a large mixing bowl, stir together mayonnaise, poultry seasoning, sage, and thyme. Add the toasted sourdough and toss gently to coat. Gradually pour in the broth mixture, stirring until the bread is soft but not mushy.
Transfer the mixture to a greased 9×9-inch glass baking dish. Spread in an even layer and bake uncovered for 30 minutes, until the top is golden brown. Serve warm.