Set 1 orange aside for now. Finely zest the 3 remaining oranges, and then cut the fruit into wedges.
Combine the orange zest with the chopped garlic from about 2 of the cloves, and the 1/2 cup of softened butter.
Gently loosen the turkey skin, and rub the butter mixture underneath it.
Combine 2 tablespoons of oil, the juice of one of the zested oranges, the remaining garlic, minced rosemary, salt and pepper in a small bowl. Use a pastry brush or your fingers to apply it all over the turkey.
Heat the remaining 1 tablespoon of olive oil in a skillet.
Saute the shallots until fragrant, or about 2 minutes.
Add the bread cubes at a high heat, and toss as you brown lightly for 2 or 3 minutes.
Add the chopped rosemary and thyme, and cook for another minute.
Remove the flesh of the 2 remaining zested oranges, making sure to catch it in a bowl.
Add the orange flesh to the bread mixture, and toss to combine.
Fill the turkey cavity with the stuffing mixture, and secure the opening.
Cut the last orange into quarters and arrange them around the bird as you place it in the roasting pan.
Bake at 325° for 3-3/4 to 4-1/4 hours, or until thoroughly cooked.
Let it stand for 10 to 15 minutes before carving.
The pan juices can be used to make gravy.