PREP THE BERRIES. In a food processor, pulse the strawberries, sugar, and vinegar in five 1-second bursts. Let stand at room temperature (go ahead and keep it in the food processor), covered, for 1 hour.
MEANWHILE, PREP THE YOGURT. If using traditional yogurt, spoon it into a fine-mesh sieve set over a deep bowl. Refrigerate to drain off the whey for 1 hour only. Discard the whey or reserve it for another use. Add the yogurt to the food processor with the strawberries. (If using Greek yogurt, do not strain, but do not add the yogurt to the berries until after they have stood for 1 hour.)
PUREE AND CHILL. Add the corn syrup to the yogurt mixture. Process until nearly smooth. Transfer to a covered container and refrigerate for at least 4 hours or overnight.
FREEZE. Freeze the mixture in an ice cream maker according to the manufacturer’s instructions. After 20 minutes, add the rosemary. Continue churning until the mixture has fully thickened and is nearly scoopable. You may eat it now, soft-serve style, but I recommend transferring it to a metal loaf pan to further chill and develop deeper flavor. Press a sheet of parchment directly on the surface of the frozen yogurt, then cover tightly with aluminum foil. Freeze for several hours.
SERVE. Let the yogurt stand at room temperature at least 20 minutes before scooping with a hot, dry scoop. Garnish sparingly with rosemary.