Whisk sugar, vanilla, and salt into the cold orange juice until dissolved. Refrigerate the sweetened juice and evaporated milk separately for at least 30 minutes.
Put the ice in a chilled pitcher and pour in the evaporated milk. While whisking continuously, add the cold orange juice in a slow steady stream.
Taste and adjust sugar if needed. Pour immediately into six tumblers, keeping ice in each glass, and garnish with orange half-slices.
Notes
Both liquids must be very cold, and the juice should be added gradually to reduce curdling.
Morir sonando is best mixed and served immediately; do not store it after combining.