Place strawberries, sugar, vanilla extract, and half-and-half in a blender; puree until smooth.
Add yogurt and pulse until combined.
Pour the mixture into an ice cream maker and freeze according to manufacturer's instructions.
Transfer half of the ice cream to a one- or two-quart lidded plastic container. Cover surface with plastic wrap and seal. For best results, ice cream should ripen in the freezer for at least 2 hours or overnight.