Heat oven to 400°F. Scrape out seeds and strings. Place squash cut-side down in 2-quart baking dish with 1 cup water. Roast, uncovered, until squash is very tender when pierced with a fork, about 40 minutes. Cool on a wire rack, reserving cooking water. When cool enough to handle, scrape pulp from skin.
Puree squash through a food mill, baby food grinder, blender, or food processor, adding up to 1/2 cup of reserved water to obtain desired consistency. Use within 1 day, or freeze for up to 1 month.
Spoon finished food into ice cube trays. Cover with waxed paper and freeze until firm. When ice cubes are frozen, remove cubes from tray and store in a resealable plastic freezer bag or freezer container. Label package with contents and date. Use within 1 month. Before serving, let thaw in the refrigerator overnight.
Heat thawed mixture to lukewarm in a small dish set in a pan of hot water. Stir before serving. Always sample a small bite to make sure the food is not too hot.
