In a heavy 3-quart saucepan, combine cream, half-and-half, and sugar. Bring to a simmer over medium-low heat; do not boil.
In a small bowl, whisk together egg yolks and strawberry extract. Add 2 cups hot cream mixture to egg mixture, whisking to combine. Whisking constantly, gradually add egg mixture to remaining hot cream mixture. Increase to medium heat, and cook for 6 to 7 minutes, until mixture coats the back of a spoon. Remove from heat, and let cool for 10 minutes.
Strain mixture through a fi ne-mesh strainer into an airtight container. Whisk in strawberry puree. Cover, and chill for 4 hours to overnight.
Pour ice-cream mixture and meringues into an ice-cream freezer. Freeze according to manufacturer’s instructions. Ice cream will be soft. For firmer ice cream, place in an airtight container, and freeze for several hours or overnight. Garnish with fresh strawberries and crushed meringue cookies, if desired.
