2 is most notable for being one of the first Bernstein pieces to be performed in public by the composer, together with his Non troppo presto.
The date of completion is a source of controversy, since it was first performed by Leonard Bernstein at the studio of Heinrich Gebhard, in Brookline, Massachusetts on June 12, 1938.
[1] However, the inscription at the end of the original manuscript reads June 14, 1938, which probably means that the composer revised the piece after performing it.
In this case, the name "Mildred" refers to Mildred Spiegel Zucker, a music teacher and childhood friend of Bernstein, with whom Bernstein had a lifelong friendship and shared a fair amount of correspondence.
2 was published relatively recently, recordings are not very well known and are typically released within cycles of complete music for piano by Bernstein.