Chop strawberries to desired size, sprinkle with 2 tablespoons of the sugar, and reserve in a bowl. You may also use a food processor on pulse to get the consistency you like.
By hand with a whisk, combine milk, remaining sugar, and salt until the sugar is completely dissolved, about 2-3 minutes. Stir in the Greek yogurt. Then stir in reserved strawberries with all their juices. Cover and place mixture in the refrigerator to chill, about 2 hours, or overnight.
Follow your ice cream maker's instructions to freeze the ice cream. I have a Cuisinart, which says to turn on the ice cream maker; pour the mixture into the freezer bowl and mix until thickened, about 15-20 minutes. The ice cream will have a soft, creamy texture and can be eaten right away if soft serve is what you like. Or, place the ice cream in an airtight container in the freezer for about 2 hours. If too hard, remove from freezer about 15 minutes before serving.