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Combine 1 tablespoon sea salt and 6 cups water in large pot and bring to boil. Gradually whisk in polenta, then cook 5 minutes over medium-high heat, whisking constantly, until polenta just begins to thicken. Stir in squash, reduce heat to medium-low, and continue to cook 30–40 minutes, stirring occasionally, until polenta is thick and no longer gritty and squash mashes easily when pressed with back of a spoon.
Mix in milk and nutmeg, increase heat to medium-high, and cook 10–15 minutes, stirring constantly and smashing squash with back of spoon until it dissolves into polenta. Remove from heat and stir in Parmesan and ¼ cup butter until melted. Let cool slightly.
Grease shallow baking dish with butter, then transfer polenta mixture to baking dish. Scatter cheddar cheese over and press down lightly with spoon to submerge. Let cool to room temperature.
Preheat oven to 375 degrees. Bake 30–35 minutes, until bubbly and lightly brown on top. Let sit 10 minutes before serving.