Preheat your oven to 375°F (190°C).
In a large skillet, heat a tablespoon of oil over medium heat, then add the diced celery and onion. Sauté until softened, about 5 minutes.
In a large bowl, combine the stale bread, sautéed vegetables, and chopped parsley, sage, salt, and pepper.
Pour in the vegetable broth, mixing gently to coat all the bread. Then, add the eggs and combine until the mixture is just held together.
Grease a muffin tin and fill each cup generously with the stuffing mixture, pressing down lightly to pack them in.
Bake in the preheated oven for 25-30 minutes, or until the tops are golden and crispy.
Allow the muffins to cool for a few minutes in the tin before transferring them to a wire rack.
Serve warm or allow to cool completely before storing in an airtight container for later use.