In PHP 8.3:

<?php
class LogEntry
{
    public function __construct(
        public readonly string $title,
        public readonly DateTimeImmutable $current,
    ) {}

    public function __clone()
    {
        $this->current = new DateTimeImmutable();
    }
}

$entry = new LogEntry("PHP Sussex is great", new DateTimeImmutable());
$newEntry = clone $entry;
?>

You can now re-assign readonly properties during clone