Sprinkle salt over the cucumber slices in a large bowl, making sure all slices get some salt. Set aside until liquid drains from cucumber slices, 3 to 4 hours. Drain liquid. Squeeze cucumber slices with paper towel to express as much moisture from them as possible.
Mix evaporated milk and vinegar together in a glass bowl until thickened. Fold cucumber slices into the milk mixture; season with black pepper.