Purists will insist on using a vanilla bean and making this recipe just like Grandma did. But the results are pretty darn good with vanilla extract and an electric ice-cream freezer
In a large saucepan heat and stir half-and-half, sugar, and vanilla bean (if using) just to a simmer. Remove from heat. Remove vanilla bean; let cool. Using a paring knife, slit vanilla bean lengthwise. Scrape out seeds. Stir seeds (or vanilla extract, if using) and whipping cream into milk mixture. Cover; chill about 4 hours.
Freeze mixture in ice-cream freezer according to manufacturer's directions. Ripen 4 hours.
Omit heating the mixture if using vanilla extract.