Preheat your oven to the highest temperature, turning on your broiler.
Clean the mushrooms with a clean and slightly damp towel.
In a bowl, pour the ingredients for the sauce and mix well. Brush the mushrooms with the sauce on both sides and put them in a pan with the stem down. Bake for 5 minutes on each side.
Meanwhile, in a deep dish, put the ingredients for the filling, except for the cheese, and mix lightly until the ingredients are slightly mixed.
Fill the mushrooms with the stuffing and sprinkle with the vegan cheese. Sprinkle all the mushrooms with olive oil and optionally, add 2 sprigs of fresh rosemary in the pan.
Bake in the grill for about 10 minutes or until the cheese melts and the tomato is slightly cooked.