Preheat oven to 325 degrees F (165 degrees C). Grease a 3-quart baking dish.
Cut bread into cubes about 3/4-inch square and spread onto a baking sheet.
Bake in the preheated oven until crisp, 12 to 17 minutes.
Heat olive oil in a large skillet over medium heat. Cook and stir onions and celery in the hot oil until soft, 8 to 10 minutes. Stir sage, thyme, salt, and black pepper into the vegetables. Mix toasted bread crumbs, chicken broth, and eggs into vegetables. Spoon dressing into the prepared baking dish and cover dish.
Bake in the preheated oven for 30 minutes, uncover, and bake until top of dressing is crisp and lightly browned, about 10 more minutes.