Core the zucchini and eggplant, then wash them well.

Wash the rice and soak it in water for 5 minutes. Drain, then mix with the ground beef. Season with salt and black pepper to taste.

Stuff the zucchini and eggplant with the rice mixture, filling each until the rice reaches just below the opening.

In a large pot, arrange the zucchini on the bottom and the eggplant on top. Sprinkle with salt and add enough water to come just above the eggplant. Place a heatproof plate on top to keep them submerged, then weigh it down with a bowl or pot filled with water.

Bring to a boil over high heat, then reduce to low and simmer until the zucchini is cooked through.