Preheat the oven to 350°F (180°C). Spread the bread cubes in a single layer on a baking sheet and toast for about 15 minutes, until dry and lightly golden. Transfer the toasted bread to a large bowl.
Grease a 12-cup muffin pan with a little butter, or line the cups with paper liners.
Heat the olive oil in a skillet over medium heat. Add the onion and celery, season with salt and pepper, and cook for about 5 minutes, until they begin to soften.
Add the turkey sausage and break it into small pieces with a wooden spoon as it cooks.
When the sausage is almost completely browned, add the chopped apple and cook for another 2 to 3 minutes.
Remove the skillet from the heat and transfer the sausage mixture to the bowl with the toasted bread.
In a separate bowl, whisk together the chicken broth, milk, and beaten egg.
Gradually pour the broth mixture over the bread, stirring gently so the liquid is absorbed evenly.
Add the dried cranberries, sage, and rosemary. Mix gently until everything is combined. The bread should be well moistened but still keep some of its texture.
Divide the stuffing mixture evenly among the 12 muffin cups. Fill each one generously and press the mixture down lightly with the back of a spoon so the muffins hold together as they bake.
Bake at 350°F (180°C) for about 25 minutes, until the tops are golden and the muffins are set.
Let the stuffing muffins rest in the pan for about 10 minutes. Carefully run a knife around the edges to loosen them, then remove from the pan.
Serve hot or warm.
