In a large pot fitted with a steamer basket, bring 2 inches of salted water to a boil. Add the eggplants; cover and steam until tender, 12 to 15 minutes. Set aside to cool completely.
Cut the eggplants in half; scoop out the flesh, leaving a 1/4-inch border in the shells. Chop the cooked eggplant and transfer to a bowl.
Combine the bread crumbs, egg, lemon zest, and garlic; season with salt and pepper. Toss the eggplant with the bread crumb mixture and the rice, peas, lemon juice, mint, and 1 cup cheese; divide the mixture among the eggplant shells (heaping ¼ cup in each) and top with the remaining cheese.
Arrange the stuffed eggplants on a large rimmed baking sheet. Broil until the cheese is browned, 5 to 8 minutes. (Alternatively, you can grill the eggplants over medium heat, covered, until the filling is set and the cheese is melted.) Sprinkle with lemon zest and mint leaves before serving.