How to Make It
Whisk together cornstarch and 1/4 cup half-and-half in a small bowl to make a slurry.
Combine sugar and remaining 2 3/4 cups half-and-half in a medium saucepan; bring to a simmer over medium. Remove from heat; gradually whisk in slurry. Return pan to medium, and cook, stirring, until mixture comes to a boil and thickens slightly, 8 to 10 minutes. Pour mixture into a heatproof bowl. Cool completely in an ice bath, about 25 minutes.
Meanwhile, use a potato masher to mash strawberries in a large bowl until crushed and juicy to yield about 3 cups strawberry puree. Stir strawberry puree into cooled half-and-half mixture. Cover and refrigerate until well chilled, at least 2 hours.
Pour half of chilled strawberry mixture into the freezer bowl of a 1 1/2-quart electric ice cream maker, and proceed according to manufacturer’s instructions.
Transfer gelato to a freezer-safe container; press a sheet of parchment paper directly on surface, and seal with an airtight lid. Place in freezer. Repeat procedure with remaining chilled strawberry mixture. Freeze gelato at least 8 hours or overnight.