Preheat the oven to 300 degrees F. Thoroughly butter or grease the muffin tin and set aside.
In a single layer, place the bread cubes on a sheet pan and bake for 10 minutes, or until barely toasted. Remove and set aside.
In a medium skillet, set over medium heat, add the olive oil. When the oil is hot, add the Italian sausage, breaking it up with a wooden spoon. Cook it until browned and thoroughly cooked, about 5 to 7 minutes. Remove from the pan and transfer to a small bowl.
Turn the heat to medium-low and if needed, add a teaspoon or two more of olive oil. Add the diced onion and celery, adding a few pinches of salt and cook until softened, about 5 to 7 minutes. Add the sage and thyme and cook for 2 to 3 minutes more, along with a few more pinches of salt and about 10 rounds of freshly ground pepper.
Add the toasted bread crumbs to a large bowl, along with the Italian sausage, cooked onion mixture and chicken broth; mix it until thoroughly combined. Do a taste test? Does it need a bit more salt? If it’s good, pour in the beaten eggs and mix one last time until combined.
Using a tablespoon, transfer mounds of the stuffing mixture to each muffin tin. Be sure to tightly pack the stuffing in each of the muffin cups. This will make sure the mixture adheres to itself and the muffins don't fall apart. You’ll end up with 9 stuffing muffins.
Bake for 35-40 minutes, until top is browned. To remove, take a butter knife and go around each of the stuffing muffins' outer edge. Using your knife, gently lift it up out of the muffin tins. Serve warm.