Rinse and dry the mushrooms, cut and remove the legs with a sharp knife. Line a baking dish with parchment and arrange the hats with the holes facing up.
Chop the chicken fillet finely. Heat a skillet with 1 tablespoon vegetable oil over medium heat, add the chopped chicken, fry for about 5 minutes, stirring occasionally.
While the chicken is roasting, finely chop the mushroom legs. Add the chopped mushrooms to the chicken skillet and cook together for another 5 minutes, stirring occasionally.
Mix flour and sour cream. Reduce heat and pour sour cream into the skillet. Season with salt, season with ground black pepper and stir. Simmer for another 8-10 minutes, until the mixture thickens, then remove from heat to cool.
Preheat the oven to 180 C. Grate feta and mix with chicken and mushrooms. Add finely chopped parsley and stir.
Spread the filling evenly over the mushroom caps. Sprinkle a little grated mozzarella on top of the filling. Bake in the oven for 15-20 minutes, then let the mushrooms cool slightly and serve.