Melt the butter in a large skillet over medium heat and throw in the mushroom caps. Toss them around for 1 minute, and then remove to a baking dish and set aside.
To the same skillet, add the olives, parsley, sun-dried tomatoes, garlic and a splash of white wine. Stir all together and cook for 1 to 2 minutes to release all the flavor. Then remove from the heat. Stir in the pine nuts.
Place a chunk of mozzarella inside each mushroom cap. Then pour the sun-dried tomato mixture over the top.
Put the baking dish in the oven and bake until the cheese has melted, about 15 minutes.
Sprinkle with the chopped basil and serve the mushrooms straight out of the oven or at room temperature.