The same day and month as the UTC day you rolled it; common years' 28 February stands in for 29 February, and 15–24 October 1582 for the ten days Rome skipped.
In Datedle, this comes up 1 in 365 a roll. It's one of 3 badges in its family, and a roll counts at most one of them.
A date a day when your dice deal it, free, no account needed.