• Preheat oven to 375 F

Make the Filling

• In large deep skillet, heat oil over medium-high heat. Add onions and cook, stirring often, until tender and golden, about 10 minutes.
• Add lamb and cook, breaking up pieces with the back of a spoon, until browned and no pink remains, about 10 minutes. Drain any fat; season with salt and pepper.
• Add garlic and tomato paste and cook for one minute. Add wine and simmer until it reduces by half. Add broth, tomatoes, eggplant and rosemary. Simmer, stirring occasionally until the sauce thickens and coats the meat, about 15 minutes. Remove from heat. Add parsley.

Make the Topping

• In large saucepan over high heat, bring water to a boil. Stir in polenta, milk and salt, stirring constantly, until smooth and polenta begins to thicken, about 15 minutes.
• Reduce heat to medium and cook until the polenta begins to bubble and pop, about 10 minutes.
• Reduce heat to low, stir in Parmesan and butter, continuing to stir until the polenta pulls away from the sides of the pan, about 10 minutes.

Assemble the Shepherd's Pie

• Spread lamb filling into a 9-x13-inch (3 L) baking dish. Drop large spoonfuls of polenta evenly over the surface of the lamb and gently spread to get an even layer.
• Bake 30 to 40 minutes until the polenta is golden and filling is bubbling around the edges.
• Let cool 10 minutes before serving.