For mushrooms:Preheat oven to 400°.
Remove stems from mushrooms.
Clean mushrooms with dry cloth or brush.
In mixing bowl toss mushrooms with remaining ingredients.
Place mushrooms upside down on baking sheets.
Cook 3 minutes.
For caramelized onions:Melt butter in heavy skillet over medium-high heat.
Sauté onions 2 minutes.
Add remaining ingredients.
Season with sea salt and freshly ground black pepper.
Bring to boil.
Reduce to simmer.
Cook until liquid is absorbed.
For assembly:Divide caramelized onions equally among mushroom caps.
Top each with one thin mango slice and blue cheese.
Bake in oven 3 to 4 minutes, until blue cheese is softened, but not melted.