Preheat oven to 375°F.
Clean the mushrooms and remove the stems. Finely chop the stems and set aside.
Cook the Italian sausage in a skillet over medium heat until browned, breaking it apart with a spatula.
Add the minced garlic and chopped mushroom stems to the skillet. Cook for another 2-3 minutes until the garlic is fragrant and the mushroom stems are softened. Remove the skillet from heat, drain excess fat and let the mixture cool slightly.
In a medium bowl, combine the cooked sausage mixture with the softened cream cheese, grated parmesan cheese, smoked paprika and 1/4 teaspoon kosher salt. Mix well until all ingredients are evenly incorporated. Taste and adjust salt as needed.
Place the mushrooms on a baking sheet. Drizzle with olive oil and sprinkle with kosher salt. Arrange cavity side up.
Spoon the sausage and cream cheese mixture into each mushroom cap, pressing slightly to pack the filling.
Bake the stuffed mushrooms in the preheated oven for 20-25 minutes, or until the mushrooms are tender and the filling is golden brown.
Remove the mushrooms from the oven and let them cool slightly. Garnish with chopped parsley if desired.