Start preparing the mushrooms for julienne. Chop them finely. Cut the onion into small cubes. Heat a frying pan with vegetable oil, fry the onion in it, then add the mushrooms. Add salt, pepper and fry until the mushrooms are ready.
Cut the boiled chicken fillet and put it in the pan with the mushrooms, fry for another 3-5 minutes. Then pour milk over the mixture and simmer for another 2-3 minutes.
Transfer the julienne into baking or cocotte dishes. Grate the cheese and sprinkle it over the julienne.
Place the dish in the oven to bake for 15 minutes. Serve the julienne to the table.