Preheat oven to 375°F.
To peel pumpkin, cut in half then scoop out seeds. Cut into wedges and carve flesh away from skin and chop into small bite-sized pieces.
For the butternut squash, cut in half across, separating the upper half from the bulbous bottom. Then, use a sharp vegetable peeler or pairing knife to trim away skin. Cut off top stem and chop into bite-sized pieces. Halve bulbous end, seed and chop.
Lightly dress pumpkin or squash in EVOO, salt, pepper and nutmeg.
Arrange pieces on a baking sheet or cooling rack set over baking sheet. Roast 35-40 minutes, until very tender. Toast the pumpkin seeds and nuts in the oven the last few minutes of roasting time.