Whisk together mixture for shaved ice: condensed milk, milk, and oat milk. Make sure that condensed milk is well-incorporated. Then place into ice cube trays and freeze for at least 8 hours until completely frozen.
Prepare fruit puree: add strawberries or mangoes and sugar into a food processor or blender. Blend until smooth. Place in refrigerator until serving time.
After shaved ice cubes are frozen solid, place them into a blender or food processor. Blend until smooth and creamy, like the consistency of a smoothie.
Serve into individual portions, and top with fruit puree and fresh strawberries (or chopped mango) and condensed milk.