Scrape vanilla-bean seeds from pod with a spoon. In a medium saucepan over medium heat, combine cream, milk, vanilla-bean pod and seeds, and 1/4 cup sugar. Heat, whisking, until small bubbles begin to appear at edge of pan. Remove from heat.
In a medium bowl, whisk egg yolks with remaining 1/4 cup sugar. Whisking constantly, pour in half of hot cream mixture and continue whisking until mixed. Pour yolk mixture back into hot cream and cook over medium heat, stirring constantly with a wooden spoon, until mixture coats back of spoon, 3 to 5 minutes. Fill a large bowl with ice and water and set nearby.
Pour custard through a fine-mesh sieve into a clean medium bowl (rinse vanilla bean pod with water and let dry on paper towels; it can be used to flavor sugar). Nest bowl in ice water and let stand, stirring occasionally, until cool, about 35 minutes. Wrap bowl tightly with plastic wrap and chill overnight.
Stir in vanilla extract and churn in an ice cream maker until softly frozen, 15 to 20 minutes. Eat right away, or transfer to a freezer-safe container and freeze until hard, at least 2 hours.
Makes about 3 cups (serving size: 1/2 cup)