Prepare a grill fire to 350° with hickory for wood smoke OR preheat oven to 375°.
Wipe mushrooms with a damp paper towel to remove any debris.
Carefully remove stems. Use a spoon to scrape gills from inside mushrooms. Chop gills and stems for filling. Set mushroom caps aside.
Cook Italian sausage in a skillet, stirring to break up until browned and crispy. Drain grease if needed.
In another skillet cook the chopped mushroom caps, gills, onions, bell peppers and garlic in 3 tablespoons of olive oil. Cook over medium heat, stirring often until vegetables are softened, about 10 minutes.
Mix cooked rice, sausage and vegetables together with 1 teaspoon of salt and 1 teaspoon of pepper.
Spray outsides of mushroom caps with olive oil, brushing to coat the entire outside surface.
Fill with sausage mixture.
Prepare the sauce in a bowl by whisking sour cream, mayonnaise, lime zest and juice, green chile powder, garlic, salt, pepper, and cumin together. Cover and refrigerate until ready to serve.
To Grill: Place stuffed mushrooms over indirect heat and cook with the grill closed about 15- 20 minutes until mushrooms are softened. To Bake: cook on a greased or lined baking sheet for 15- 20 minutes.
Serve immediately with creamy green chile sauce and garnish with cilantro if desired.