How to Make It
Preheat the oven to 400°. Butter a shallow, 3-quart baking dish. Thinly slice the bulbous parts of the squash into crescents and arrange them in a single layer on a rimmed baking sheet. Cut the necks of the squash into 1/2-inch cubes and spread them on another baking sheet.
In a small bowl, combine the butter and olive oil. Lightly brush the squash crescents with the butter mixture and season with salt. Drizzle the remaining butter over the diced squash and sprinkle with salt, nutmeg and cinnamon. Roast the squash for about 10 minutes, turning once, until softened and lightly browned in spots. Drizzle with the maple syrup and roast for 5 minutes longer. Let cool.
In a bowl, whisk the half-and-half with the eggs, grated cheese and a pinch each of salt and pepper. Add the bread and squash cubes; toss gently. Spoon the mixture into the prepared baking dish and arrange the squash crescents on top. Bake the bread pudding for 1 hour, until the top is golden in spots and the center is firm. Let cool for 15 minutes before serving.