Preheat oven to 375 degrees F. Spray a rimmed baking sheet with cooking spray and set aside.
Wipe mushrooms clean with paper towels. Remove stems and dice. Hollow out the caps if necessary. Brush each cap with olive oil.
In a large skillet over medium heat add 2 tablespoons olive oil and mushroom stems, cook for 1 minute and then add sausage; breaking up any clumps. Saute for 3 minutes. Add the leeks and saute for another 3 minutes or until sausage is completely browned and leeks are tender. Remove from pan and set aside.
In a medium bowl, combine stuffing mix and hot broth. Let sit for 2 minutes or until slightly softened.
Stir in browned sausage mixture, sage, garlic, and 2 tablespoons Parmesan into stuffing.
Fill each mushroom with stuffing mixture and arrange caps on prepared baking sheet. Sprinkle mushrooms with remaining 2 tablespoons of Parmesan.
Bake in preheated oven for 20 to 25 minutes, or until golden. Serve immediately.