Heat a frying pan with vegetable oil and fry the onion, carrot and mushrooms until soft.
Mix the minced meat with rice, then add the fried vegetables.
Line a baking dish with zucchini slices, allowing the edges to extend 5 cm beyond the edge of the dish. Spread the filling over the dish, add salt and pepper to taste, then cover the dish with the protruding zucchini slices. Spread the remaining zucchini on top.
Spread grated cheese over the pie and bake in an oven preheated to 190°C for 40-50 minutes.