Preheat oven to 350°. Rinse a 3- to 9-pound Sugar Pie (also called Sugar), Long Island Cheese, Apple Blossom, or Jarrahdale pumpkin or kabocha squash. With a large, heavy knife, cut in half vertically, starting along one side of stem. Use a mallet or hammer to tap knife gently through flesh. Scoop out and discard seeds, or reserve for another use. Rub the inside with about 2 teaspoons vegetable oil and lay, cut side down, in a 12- by 16-inch rimmed baking pan. Bake until squash is soft when pressed, 45 to 75 minutes.
Scoop out flesh, place in a bowl, and mash with a potato masher. If pumpkin is watery, place pumpkin in two colanders lined with cheesecloth. Let stand, lightly pressing, until dripping stops, 15 to 30 minutes. (Draining is critical for baked goods, but less so for soup.) Most meaty pumpkins yield 3/4 to 1 1/4 cups mashed pumpkin per pound of raw weight. Chill airtight up to 3 days or freeze up to 6 months.