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1
Heat 1 tbsp of the olive oil in a small saucepan over medium heat; when it is hot add the shallot, carrot, garlic, and rosemary, and cook until the vegetables are soft (about 5 minutes).
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2
Add the lentils and stock and stir.
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3
Bring the mixture to a boil, then cover the pot and turn the heat down to a simmer. Cook until the lentils are tender (about 40 minutes).
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4
Peel the potatoes and chop them into large pieces. Bring a medium pot of water to a boil and add the potatoes; cook until they are tender (about 20 minutes). When they are done, remove them and set aside until you are ready to mash them.
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5
Keep an eye on the potatoes and lentils while you prepare the mushrooms and onions; if either is done before you are ready you can just take them off the heat and set aside.
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6
To cook the mushrooms, heat another tablespoon of oil in a medium skillet over medium heat. When it is hot, add the mushrooms and thyme and season with salt and pepper. Cook until all the liquid has evaporated and the mushrooms are browned (about 10 minutes).
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7
Discard the sprigs of thyme and remove the mushrooms to a plate.
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8
Heat the final tablespoon of olive oil in the same skillet over medium heat and and caramelize the onions. Cook the onions until they are very soft and golden brown. When the pan gets dry and the onions begin to stick, deglaze the pan with a splash of the wine, scraping up all the flavorful bits. Add the vinegar on the final deglazing. Season with salt and pepper.
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9
Meanwhile, your potatoes should be ready. Put them in a large bowl and add 1 tbsp of the butter, the milk, and some salt and pepper. Use a potato masher, a ricer, or a hand mixer to mash them to your desired consistency, then stir in 1/4 cup of the parmesan.
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10
In the largest pot or bowl that you are using, combine the lentils, mushrooms, and onions, and stir in the remaining tablespoon of butter and 1/4 cup parmesan. Pour the mixture into a baking dish (we used 2 5 inch rounds for individual servings). Spread the mashed potatoes evenly over the top.
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11
Turn the broiler on high and put the dish under the broiler until the potatoes begin to turn crispy and brown (5-10 minutes, depending on your broiler).
