Preheat your oven to 300°F.
Toast the bread cubes for about 8 to 10 minutes until they are dry and slightly crunchy.
Increase the oven temperature to 350°F.
Heat the oil in a sauté pan over medium heat. Add the chopped sausage and cook for about 4 to 5 minutes until slightly golden. Remove from the heat and set aside to cool.
In the same sauté pan, melt the butter, then add the diced onions and sauté for about 3 minutes until softened. Add the diced celery, chopped apples, and thyme, cooking for another 5 minutes until everything is heated through. Let cool.
In a large mixing bowl, combine the cooled sausage, toasted bread cubes, and cooled sautéed mixture. Toss gently.
Grease muffin tins and scoop the stuffing mixture into each cup, filling them to the top and packing it down firmly.
Bake in the oven for about 45 minutes until the tops are golden and crispy.
Allow to cool in the muffin tin for about 10 minutes before removing them.