Heat a grill pan (or the grill) over medium high heat and drizzle with olive oil. Once hot, add the mushrooms and grill on each side for about 4 minutes.

In a medium bowl, mix together the sun dried tomatoes, feta, dill, olives, and about 1 teaspoon of olive oil. Season with pepper if desired (no need for salt – the olives and feta are very salty!).

Remove the mushroom caps from the grill, turn upside down and stuff with this mixture.

Place on baking dish, top with shredded cheese, and cook under the broiler for about 5 minutes, until the cheese is melted and golden brown.

Serve immediately.