Into a blender, add the cold water, lime wedges, and granulated sugar. Blend until smooth and the lime wedges are blended.
Place a fine mesh strainer over a bowl and pour the blender contents into the strainer, making sure to catch the liquid below in the bowl.
Discard the lime pulp and pieces that are left in the strainer.
Rinse out the blender. Pour the strained lime juice mixture (from the bowl) back into the blender. Add the sweetened condensed milk.
Blend again until smooth and it's frothy.
Fill a glass with ice and pour the Brazilian lemonade over top. Garnish with slices of fresh lime.