Preheat the oven to 400°F. Line a baking sheet with parchment paper.
Remove stems from the mushrooms; finely chop the stems and set them aside. Next, gently scrape out the insides of the mushrooms and set them aside.
Into a large skillet over medium heat, add the oil. When the oil is hot, add chopped mushroom stems and onion. Cook for 3 minutes, until vegetables are softened.
Stir in parsley, basil, and sherry. Simmer for 3-5 minutes, until the liquid is absorbed. Remove from heat and allow to cook for 5 minutes.
Stir in the cheeses.
Generously fill each of the mushroom caps and set at least 1-inch apart on the baking sheet.
Bake for 12 minutes, or until the cheese is melted.