Wash mushrooms and remove their stalks. Place them in a baking tray and pour in 1 cup of water. Get them slightly toasted at 392°F (200 °C) until semi-cooked. Cut the stalks into very small pieces. In a deep pan, heat the olive oil, sauté the chopped stalks and, once semi-cooked, add the finely chopped green onions and ham and stir.
Remove the stuffing from the heat and once cool, grate the blue cheese on top. Remove the mushrooms from the oven and pour out the water, which has accumulated during baking. Distribute the mixture evenly in all the mushrooms. Top with a thick piece of blue cheese. Fry the mushrooms until the cheese is lightly browned.
Serve on arabic pitas, and sprinkle each mushroom lightly with a little paprika.