Preheat oven to 400°F (205°C).
Brush the cut sides of the butternut squash with oil.
Place the squash cut-side down on a parchment-lined baking sheet.
Roast for 25–35 minutes, then flip the squash cut-side up.
Continue roasting for another 20–30 minutes, or until the squash is very soft.
In a small bowl, whisk together the melted butter, brown sugar, cinnamon, nutmeg, ginger, and salt.
Scoop the roasted squash into a mixing bowl or food processor.
Add the butterscotch mixture and purée until smooth and velvety.
Reduce oven temperature to 375°F (190°C).
Transfer the squash purée to a baking dish and smooth the top.
Bake for 20–30 minutes, or until the edges caramelize and the top deepens in color.
If using the crumble topping, mix the breadcrumbs or pecans with brown sugar, melted butter, and cinnamon.
Sprinkle the crumble over the squash halfway through the second bake.
Continue baking until the crumble is golden and crisp.