Heat the oven to 425°F. On a rimmed baking sheet, toss the butternut squash with 2 tbsp olive oil, 1 tsp of the kosher salt, and 0.5 tsp of the black pepper. Roast, turning once, until tender and caramelized at the edges, 25–30 minutes.
Meanwhile, in a skillet over medium heat, melt 2 tbsp butter. Add the shallot and cook until translucent, 3–4 minutes. Stir in the garlic and sage and cook until fragrant, 1 minute; remove from heat.
In a medium saucepan over medium heat, melt the remaining 6 tbsp butter. Whisk in the flour and cook, whisking constantly, 2 minutes. Gradually whisk in the milk until smooth; bring to a gentle simmer and cook, whisking, until thick enough to coat the back of a spoon, 6–8 minutes. Season with the remaining 1 tsp kosher salt, remaining 0.5 tsp black pepper, and the nutmeg.
Cover the dish tightly with foil (tent it so it doesn’t touch the cheese) and bake until bubbling at the edges, 25–30 minutes. Uncover and bake until the top is deeply golden and lightly crisp, 15–20 minutes more. Let rest 15 minutes before slicing and serving.