Whisk the creams together in a bowl, then whisk in the sugar until dissolved. Add the vanilla bean and extract, whisking to blend. Cover the bowl with plastic wrap and refrigerate for 2 hours. Remove the vanilla bean and scrape out the inside of the bean with the back of a knife. Return these flecks of vanilla to the cream and whisk to blend; discard the bean. Prepare the ice cream in an ice-cream maker according to manufacturer's directions. Store the ice cream in the freezer, where it has a shelf life of about 1 week.