Preheat oven to 425°F. Combine strawberries, vanilla, salt and sugar in a 13x9x2" baking pan.Roast berries, stirring occasionally, until juices are bubbling, 15-20 minutes. Let cool.
Purée berries, juices and remaining ingredients in a blender until smooth. Process mixture in an ice cream maker according to manufacturer’s instructions until the texture of soft serve ice cream. Transfer mixture to an airtight container,press a piece of parchment or plastic wrap against the top of the yogurt to prevent ice crystals from forming.Freeze until ready to serve.