In 2-quart saucepan, place strawberries, brown sugar and thyme sprigs. Cook over medium-low heat 20 minutes or until strawberries begin to fall apart. Remove from heat; remove and discard thyme.
Meanwhile, in 1-quart saucepan, heat granulated sugar, water, lemon juice and salt to boiling; boil 1 to 2 minutes or until sugar is dissolved. Stir sugar syrup into strawberry mixture. Cool 1 hour.
In blender, place half of strawberry mixture. Cover; blend on high speed until smooth. Pour into 3-quart ice-cream freezer. Repeat procedure with remaining strawberry mixture. Add yogurt and vanilla to ice-cream freezer; stir well with whisk. Freeze according to manufacturer’s directions. Spoon mixture into freezer container. Cover; freeze 1 hour or until firm.