1. Preheat oven to 375°. Cut pumpkin in half, using a large, heavy knife and a mallet to tap knife through flesh. Scoop out and discard seeds. Rub inside of pumpkin with oil. Set pumpkin cut side down on a rimmed baking sheet.
2. Bake until very soft when pierced, at least 45 minutes (up to 75 minutes for a very large squash). Scoop out flesh into a food processor and whirl until smooth. If purée is watery, drain in a fine strainer about 30 minutes.
Make ahead: Chill up to 3 days, or freeze up to 6 months.
Note: Nutritional analysis is per 1/4-cup serving.