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Bring 1 inch of water to a boil in a large pot fitted with a steamer basket. Add potatoes, cover and cook until tender, 10 to 15 minutes.
Meanwhile, heat oil in a large pot over medium-high heat. Add onion and cook, stirring often, until softened, 3 to 5 minutes. Stir in garlic and ½ teaspoon each salt and pepper; cook until fragrant, about 30 seconds. Add broth, tomatoes and lentils and bring to a simmer over high heat. Adjust heat to maintain a simmer, cover and cook until the lentils are tender, 15 to 20 minutes. Stir in kale. Remove from heat and cover to keep warm.
Drain the potatoes and return them to the pot; add milk, butter and the remaining ¼ teaspoon each pepper and salt. Mash to desired consistency. Stir in Parmesan.
Serve the stew over the mashed potatoes.