Put 2 cups of chopped strawberries in a medium saucepan along with 1 of cup water and the sugar. Bring everything to a boil, then turn the heat down to low. Cook while stirring occasionally until the sugar dissolves and the strawberries have softened, about 2 minutes. Take the pan off the heat and let it cool until it's no longer steaming hot, about 10 minutes.

Pour the cooked strawberries and syrup into a blender or food processor and purée until they turn smooth. Let the mixture cool completely (feel free to put it in the fridge to speed this process up).

For each serving, fill a 12- to 14-oz. cup or glass halfway with shaved ice and pour in about a 1/3 cup strawberry syrup. Fill the cup with more shaved ice and pour in another 1/3 cup syrup. Top it off with 2 tbsp. chopped strawberries and, if you like, pour on 1 tbsp. condensed milk. Serve with a spoon and/or a fat straw.