In Italian gelato shops, a stracciatella describes an ice cream that has chocolate mixed into it -- as our recipe does.
Put 4 cups water, 4 cups sugar, and the lemon juice in a large saucepan. Scrape in the vanilla seeds, then add the bean. Bring mixture to a boil.
Reduce heat to medium. Add pears to pan. Cover surface of liquid with a sheet of parchment paper. Cook pears until very tender, 15 to 25 minutes (time will vary depending on ripeness of pears). Remove from heat. Let pears cool completely in poaching liquid.
Transfer pears to a cutting board. Discard all but 1/4 cup poaching liquid. Halve and core pears. Puree 3 pears in a food processor. Finely chop remaining 2 pears.
Whisk yolks, remaining 1/4 cup sugar, and the salt in a medium bowl; set aside.
Heat milk and cream in a medium saucepan over medium-high heat until mixture is steaming and small bubbles form on edges. Add to yolk mixture; whisk until combined. Pour mixture back into pan; cook over low heat, stirring constantly with a wooden spoon, until thick enough to coat spoon, about 5 minutes.
Pour custard through a fine sieve into a large bowl set in an ice-water bath. Let cool, stirring occasionally.
Stir pear puree, reserved poaching liquid, brandy (if desired), and extract into custard. Freeze in an ice-cream maker according to manufacturers instructions.
When mixture is frozen but still being churned, add chopped pear. Pour in melted chocolate in a slow, steady stream; mix until combined. Serve with dark-chocolate syrup.
Ice cream can be frozen, in an airtight container, up to 2 days.