Heat oven to 425 degrees F. Toss 2 cups strawberries (cleaned and cut into quarters) with 1 Tablespoon sugar and 1 Tablespoon balsamic vinegar. Roast in a 9 x 13 pan or a baking pan lined with aluminum foil for 18-22 minutes. Let cool completely before combining with the base.
Chill the base ingredients then combine and stir in a large bowl. Fold in the cooled strawberries. Pour into the ice cream machine and process for 18-20 minutes. Transfer the almost frozen ice cream into a container and freeze for at least 4 hours.