Place 2 pounds of hulled strawberries (reserve 1/2 pound for later) and 1 cup of cold water into a blender. Blend until the mixture is completely smooth and pureed.
Pour the blended strawberry mixture through a fine-mesh sieve into a bowl or large pitcher to remove the seeds and pulp, pressing gently to extract as much liquid as possible.
In a large pitcher, combine the strained strawberry liquid from Step 2, 4 cups of whole milk, the can of sweetened condensed milk, and the remaining 3 cups of cold water. Stir thoroughly until everything is well blended. Optionally, finely chop the reserved 1/2 pound of strawberries and add them to the pitcher for some fruity texture—I like to add the fresh pieces for extra bursts of strawberry flavor.
Cover the pitcher and chill the strawberry milk mixture in the refrigerator until very cold, at least 1 hour. When ready to serve, fill tall glasses with ice cubes, pour the chilled strawberry milk over the ice, and enjoy this refreshing drink.