Place bread in a large bowl and fill it up with water, making sure to completely submerge the bread.
Next, in a large saute pan with 1 tablespoon of olive oil on medium-high heat cook the Italian sausage until it completely cooked through. Using a spoon, break up the sausage while it is cooking so that any large chunks are broken up. Once the sausage is cooked, place in the refrigerator to cool.
Remove the bread from the water and squeeze the bread until all of the liquid is out. Place the bread in a large bowl along with the cooled Italian sausage, rosemary, Parmesan cheese, bread crumbs, eggs, salt and pepper and mix until completely combined and set aside.
Rub the mushroom caps down with the 3 tablespoons of olive oil and season them on all sides with salt and pepper and place them cap side down in a 13x9 Reynolds(R) Bakeware pan. Take a small amount of stuffing and stuff each mushroom until the stuffing is all gone. Once they are all stuffed, top off with the remaining 1/4 cup of Parmesan cheese and bake in the oven for 25 minutes. Take bakeware out of the oven and allow to cool for 5 minutes. Serve hot.