Preparation Heat oil in heavy large skillet over medium-high heat. Add onion, basil, garlic, and rosemary. Sauté until onion softens, about 5 minutes. Transfer to medium bowl; mix in shrimp, breadcrumbs, cheese, and mayonnaise. Season filling to taste with salt and pepper. Arrange mushrooms, rounded side down, on oiled baking sheet. Mound shrimp filling in mushrooms, pressing filling to compact slightly. (Can be made 6 hours ahead. Cover and refrigerate.) Preheat oven to 350°F. Bake mushrooms until tender and filling begins to brown, about 35 minutes. Serve hot.
Preparation Heat oil in heavy large skillet over medium-high heat. Add onion, basil, garlic, and rosemary. Sauté until onion softens, about 5 minutes. Transfer to medium bowl; mix in shrimp, breadcrumbs, cheese, and mayonnaise. Season filling to taste with salt and pepper. Arrange mushrooms, rounded side down, on oiled baking sheet. Mound shrimp filling in mushrooms, pressing filling to compact slightly. (Can be made 6 hours ahead. Cover and refrigerate.) Preheat oven to 350°F. Bake mushrooms until tender and filling begins to brown, about 35 minutes. Serve hot.