Clean mushrooms with damp paper towl. 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.