Cheesy Baked Butternut Squash Polenta

Combine 1 Tbsp. salt and 6 cups water in a large pot and bring to a boil. Gradually whisk in polenta, then cook over medium-high heat, whisking constantly, until polenta just begins to thicken, about 5 minutes. Stir in squash, reduce heat to medium-low, and continue to cook, stirring occasionally, until polenta is thick and no longer gritty, and squash mashes easily when pressed with the back of a spoon, 30–40 minutes.
Mix in milk and nutmeg, increase heat to medium-high, and cook, stirring constantly and smashing squash with the back of spoon, until squash is dissolved into the polenta, 10–15 minutes. Remove from heat and stir in Parmesan and 1/4 cup butter until melted. Let cool slightly.
Meanwhile, heat oil in a large skillet over medium-high until shimmering. Add sage and cook, stirring, just until leaves are lightly crisped and darker in color, about 1 minute. Using a slotted spoon, transfer sage to a paper towel-lined plate to drain.
Grease a shallow 3-qt. baking dish with butter, then transfer polenta mixture to baking dish. Scatter Fontina cheese over and press down lightly with spoon to submerge. Top with crisped sage. Let cool to room temperature, then cover and chill overnight and up to 2 days.
Preheat oven to 375°F. Uncover dish and bake casserole until bubbly and lightly browned on top, 30–35 minutes. Let sit 10 minutes before serving.