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1
Heat 1/4 cup of olive oil in heavy large skillet over medium-high heat. Add onion, basil, garlic, and rosemary. Saute until onion softens, about 5 minutes.
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2
Transfer to medium bowl; mix in shrimp, crab, 2/3 cup panko breadcrumbs, Parmesan cheese, and mayonnaise. Season filling to taste with salt and pepper. Set aside.
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3
Break off any mushroom stems. Using a spoon, gently scrape dark gills out of the inside of the mushrooms.
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4
In a small bowl, break egg and add a bit of water to make an egg wash. Dip round side of Portobello mushrooms into egg wash, then press onto plate with remaining 1/3 cup panko breadcrumbs (doesn't have to be completely covered in breading).
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5
Using the same pan you just sauteed the onion mixture in, and adding a bit more olive oil to the pan, fry mushrooms breadcrumb side down just until the panko is slightly browned, about 3-5 minutes. (Don't make them too brown as the breadcrumbs will continue to brown as the dish bakes in the oven.)
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6
Arrange mushrooms, rounded side down, in baking dish. Mound crab/shrimp filling into cleaned inside of mushrooms, pressing filling to compact slightly. (Can be made 6 hours ahead. Cover and refrigerate.)
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7
Preheat oven to 350u00b0F. Mix together the shredded mozzarella and Asiago cheese. Sprinkle tops of mushrooms with the shredded cheese mixture and bake until tender and filling begins to brown, about 35 minutes.
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8
Serve hot.
