Put the cold water, lime wedges, and sugar into your blender and pulse until the limes are thoroughly mixed in.
Set a fine mesh strainer over a bowl and pour the blended mixture through it to separate the liquid from the pulp.
Throw away the solids left in the strainer and rinse your blender clean.
Return the strained lime liquid back into the blender, then add the sweetened condensed milk.
Blend everything together until the drink is smooth and frothy.
Fill glasses with ice and serve the Brazilian lemonade over it. Add lime slices to garnish if desired.
