Dress the mushroom caps with liberal drizzle of extra-virgin olive oil and season with salt and pepper. Broil the portobello mushrooms 5 minutes on each side until tender.
While caps are broiling heat 1 tablespoon extra-virgin olive oil in a skillet over medium high heat, add sausage and brown and crumble the meat, then add tomatoes to skillet and cook another few minutes until they burst. Add cream to skillet and reduce 2 to 3 minutes more. Remove the sausage from heat and fold in basil. Fill mushroom caps and top with cheese, place under broiler to brown 2 to 3 minutes then quarter caps and serve.