Put 2 cups strawberries in a medium saucepan with 1 cup water and the sugar. Bring to a boil, then reduce heat to low. Cook, stirring occasionally, until sugar dissolves and strawberries are soft, about 2 minutes. Remove from heat and let cool until no longer steaming hot, about 10 minutes.
Pour cooked strawberries and syrup into a blender or food processor and purée until smooth. Let cool completely (you can put it in the refrigerator to speed this up).
For each raspado, fill a 12- to 14-oz. cup or glass halfway with shaved ice and pour in about 1/3 cup strawberry syrup. Fill cup with more shaved ice and pour in another 1/3 cup syrup. Top with 2 tbsp. chopped strawberries and pour on 1 tbsp. condensed milk if you like. Serve with a spoon and/or a fat straw.
Make ahead: Syrup, chilled, up to 5 days. Shaved ice, frozen, up to 1 day (whirl again before serving to break up icy clumps).