Vegetarian Butternut Squash and Swiss Chard Polenta Lasagna

Heat the oven to 450°F and arrange a rack in the middle.

Heat 2 tablespoons of the oil in a large saucepan over medium heat until shimmering.

Add 1/3 cup of the shallots, the rosemary, and thyme, season with salt, and cook, stirring occasionally, until the shallots are softened, about 4 minutes.Increase the heat to high, add the measured water, milk, and measured salt, stir to combine, and bring to a simmer. Reduce the heat to low and, while whisking constantly, slowly pour in the polenta in a thin, steady stream until all of it is incorporated and there are no lumps.Cook, whisking or stirring with a wooden spoon occasionally, until the polenta pulls away from the sides of the pan and the grains have softened, about 35 to 40 minutes. (If the polenta starts to get too thick before it’s done, add water 1/4 cup at a time as necessary.) Meanwhile, prepare the squash.Using a vegetable peeler, peel the squash, then trim the ends.

Cut it in half lengthwise and remove the seeds.

Cut each half crosswise into 1/4-inch-thick slices.

Place the slices in a large bowl, add 2 tablespoons of the oil, season generously with salt and pepper, and toss with your hands to evenly coat.

Spread the squash in an even layer on a baking sheet. Roast until knife tender, about 20 minutes. Wipe out the bowl and set it aside (no need to wash it). When the squash is ready, transfer it to a wire rack to cool. Reduce the oven temperature to 375°F.When the polenta is ready, stir in the Gruyère cheese until it’s melted and evenly incorporated. Taste and season with salt as needed.

Transfer the polenta mixture to a 17-by-12-inch rimmed baking sheet. Using a rubber spatula, spread it into an even layer; set aside.

Heat the remaining 2 tablespoons of oil in a large frying pan over medium heat until shimmering.

Add the remaining 1/3 cup of shallots, season with salt and pepper, and cook, stirring occasionally, until softened, about 4 minutes. Increase the heat to medium high, add the wine, and cook until it has almost evaporated, about 3 to 4 minutes.

Add the chard, season with salt and pepper, and cook, tossing constantly with tongs, until it’s completely wilted and tender and the liquid has almost evaporated, about 3 to 5 minutes.

Transfer the mixture to a colander in the sink and let it sit, stirring occasionally, until it’s cool enough to handle, about 10 minutes.When the chard mixture has cooled, squeeze large handfuls to release any excess liquid and transfer to a cutting board. Finely chop and place in the reserved bowl.

Add the ricotta and 3/4 cup of the Asiago and stir to combine. Taste and season with salt and pepper as needed.

Cut the polenta in half crosswise (you should have 2 pieces that are approximately 8 by 6 inches each). Using a flat spatula, transfer 1 of the halves in large pieces to a 13-by-9-inch baking dish and, using your hands, press into an even layer to completely cover the bottom of the dish. Using a rubber spatula, evenly dollop half of the ricotta mixture over the polenta and spread it into an even layer. Evenly shingle half of the squash pieces over the ricotta mixture. Repeat the layers once more with the remaining halves of the polenta, ricotta mixture, and squash.

Sprinkle with the remaining 1/4 cup of Asiago cheese.

Bake until the cheese is melted and the top is golden brown, about 30 to 40 minutes.