Clean mushrooms with damp paper towel. Remove mushroom stems; finely chop stems and set aside. Saute mushroom caps in butter in skillet until almost tender; drain on paper towels.
Saute mushroom stems and red pepper in skillet. Add cream; bring to a boil. Reduce heat and add cheese; cook until melted.
Stir in rice, basil, and pepper; cook until thoroughly heated. Spoon rice mixture into mushroom caps. Place mushroom caps in greased shallow baking pan.
Cover and bake at 350 F for 10 minutes or until tender. Drain on paper towels. Garnish stuffed mushrooms with basil.