Shrimp Stuffed Portabello Mushrooms

1/4 cup olive oil 1/2 cup chopped onion 1/4 cup chopped fresh basil 3 large garlic cloves, chopped 1/2 teaspoon chopped fresh rosemary 6 ounces cooked bay shrimp 2/3 cup fresh breadcrumbs made from crustless French bread 1/2 cup grated Parmesan cheese 1/4 cup mayonnaise 8 2 to 2 1/2-inch portobello mushrooms, dark gills removed

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, bread crumbs, 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 425°F. Bake mushrooms until tender and filling begins to brown, about 20 minutes. Serve hot.