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1
To prepare the Bolognese sauce: Heat the peanut oil in a large skillet over medium heat until it moves easily across the pan.
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2
Add the onion, carrot, celery, salt, and pepper and cook, stirring occasionally, until the vegetables begin to soften, about 5 minutes.
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3
Add the garlic, cook for 1 minute, then add the mushrooms and thyme leaves.
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4
Cook, stirring frequently, until the mushrooms are almost tender, about 3 minutes.
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5
Add the tomato, cook for about 2 minutes more, then add the stock 2 tablespoons at a time, bringing the pan to a simmer before each addition.
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6
Simmer the Bolognese until it is concentrated but not yet dry, about 30 minutes.
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7
Set aside to cool.
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8
To make the polenta: Moisten the polenta with 2 tablespoons of water, mixing well with your hands.
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9
Bring 4 cups of water to a boil in a saucepan over high heat.
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10
Add a pinch of salt and gradually stir in the polenta.
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11
Stirring constantly, bring the polenta to a boil, then reduce the heat to low.
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12
Cook the polenta, stirring occasionally, until it is no longer grainy, about 30 minutes.
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13
Stir the olive oil into the polenta, season with salt, and remove it from the heat.
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14
To assemble the gratin: Heat the oven to 350F.
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15
Spoon half the polenta into a medium baking dish and cover with half of the sauce.
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16
Spoon in the remaining polenta, spread it evenly, then sprinkle with the Parmigiano-Reggiano.
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17
Transfer the remaining sauce to a small saucepan and reserve.
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18
Bake the gratin until the top is golden, about 40 minutes.
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19
Just before serving, warm the reserved sauce over low heat.
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20
Divide the gratin and sauce among 4 plates and serve.
