Puree the 1½ cup strawberry with a hand blender. Place it in a small pot and combine the strawberry with sugar.
Heat the strawberry mixture over medium heat until it comes to a boil and let it simmer for 10-15 minutes. After 15 minutes, add cubed strawberry and let it simmer again for 3 minutes. Keep stirring to prevent it from burning. Turn off the heat and let it cool.
Place half of the strawberry puree into each glass and swirl it around to make a pattern, then add ice and milk.
Garnish the strawberry milk with fresh strawberry. Serve immediately. Enjoy!