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.