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1
Preheat the oven to 400 and lightly oil a baking sheet.
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2
Arrange the eggplants, cut side down, on the baking sheet and bake for 20 minutes, or until softened but not falling apart.
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3
Meanwhile, bring a small saucepan of salted water to a boil.
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4
Add the potato and cook until crisp-tender, about 5 minutes; drain.
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5
Heat 1 tablespoon of the olive oil in a large skillet.
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6
Add the onion and cook over moderately high heat for about 5 minutes, stirring occasionally, until softened.
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7
Add the lamb and cook, stirring occasionally to break up the meat, until no liquid remains and the lamb is beginning to brown, about 10 minutes.
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8
Add the potato and stock and cook over moderate heat until the mixture is dry and the potato is tender, about 8 minutes.
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9
Heat the remaining 1 tablespoon of olive oil in a large nonstick skillet.
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10
Add the eggplants, cut side down, and cook over high heat until browned, 1 to 2 minutes.
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11
Transfer to a work surface and let cool.
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12
Carefully scoop the flesh out of each eggplant, leaving a 1/4-inch-thick shell.
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13
Chop the eggplant flesh.
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14
Add the eggplant and tarragon to the lamb mixture and season generously with salt and pepper.
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15
Lightly oil a large baking dish.
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16
Arrange the eggplant shells in the dish and fill with the lamb mixture, mounding slightly.
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17
Sprinkle with the Parmesan and bake for about 10 minutes, until the filling is heated through and the cheese is melted.
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18
Preheat the broiler and broil for about 1 minute, until lightly browned.
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19
Transfer the eggplants to a platter and serve.
