Preheat the oven to 375°F (190°C).
In a large skillet, heat 2 tablespoons of oil over medium heat and sauté the diced onions until translucent, about 5 minutes. Then, add the diced celery and cook for another 3 minutes.
In a large bowl, combine the cubed bread, sautéed onions and celery, sage, thyme, black pepper, and beaten egg. Mix until fully incorporated.
Gradually pour in the broth, mixing gently until the bread is just moist but not soggy.
Lightly grease a muffin tin with non-stick spray or butter. Fill each muffin cup halfway with the stuffing mixture, then use a teaspoon to add a generous spoonful of gravy to the center.
Top each muffin with more stuffing mixture until cups are filled to the brim, pressing gently to compact the mixture.
Bake for 25–30 minutes, or until the edges are golden brown and the tops are firm to the touch.
Let the muffins cool in the tin for 5 minutes before gently removing them and transferring to a wire rack to cool slightly before serving.