Remove stems from mushrooms. Set aside caps. Finely chop stems, discarding hard pieces.
Heat olive oil in a medium saucepan over medium heat. Stir in mushroom caps, garlic and green onions. Cook and stir until soft, about 4 minutes. Remove from heat and allow to cool until easily handled.
In a medium bowl, mix together chopped mushroom stem pieces, cream cheese, port wine, Italian-style seasoning, Parmesan cheese, Cheddar cheese, ground black pepper and hot pepper sauce.
Stuff mushroom caps with the mushroom stem mixture. Arrange on a medium baking sheet and bake in the preheated oven 20 to 25 minutes, or until lightly browned.