Combine squash and milk in heavy small saucepan. Scrape in seeds from vanilla bean; add bean. Bring to simmer over medium heat. Partially cover, reduce heat to medium-low, and simmer until the squash is very tender, about 20 minutes. Remove vanilla bean. Drain the squash and place in a food processor. Blend until smooth. DO AHEAD: Can be made 1 day ahead. Cover and chill.
Preheat oven to 375°F. Spray six ¾-cup ramekins with nonstick spray. Place 1/2 cup of the squash puree in large bowl (reserve remaining puree for another use). Add sugar, oil, cider, and egg to puree and beat to blend. Sift flour, cinnamon, baking soda, and salt over; beat to blend until just mixed. Divide batter among prepared ramekins.
Bake cakes until tester inserted into center comes out clean, about 18 minutes. Cool cakes in ramekins. Turn out onto plates. Dust with powdered sugar or beat brown sugar cream to firm peaks and spoon alongside cakes.