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 or until mixture coats the back of a spoon. Remove from heat, and let cool for 10 minutes.
Strain mixture through a fine-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 air- tight container, and freeze for several hours or overnight. Garnish with fresh strawberries and crushed meringue cookies, if desired.
