Preheat oven to 400 F degrees.
Pull stems from portobello mushroom caps. Using the tip of a teaspoon, gently scrape off and discard black gills from under side of portobello caps. Rub 1 tbsp of the olive oil over the portobello caps and place cupped side up on a baking sheet. Bake in center of oven for 20 minutes.
In the meantime, in a large bowl, mix the rest of the ingredients together and toss.
Let mushrooms cool. When cooled, stuff the portobello mushrooms with the feta cheese mixture, sprinkle additional basil if desired and serve.