Preheat the oven to 350 degrees . Spread out the bread cubes on a parchment-lined baking sheet and toast until lightly browned, 10 to 15 minutes.
In a large saucepan or skillet, combine 2 tbsp. butter and the EVOO over medium-high heat. Add the onion and celery pieces (reserving the leaves) and cook until softened, about 8 minutes.
Add the apple, toasted bread and celery leaves to a large bowl. Scrape in the onion-celery mixture. Stir in the remaining 4 tbsp. butter and 3 cups chicken broth, adding more if needed to coat well; season with salt and pepper. Let the mixture cool slightly, then stir in the eggs, parsley and sage.
Grease a medium shallow baking dish. Add the stuffing and spread evenly into the dish. Bake until browned and crisp, 25 to 30 minutes.
