Milonga de mis amores was written by Pedro Laurenz in 1937 and has been recorded by several orquestas, including Francisco Canaro and Juan D’Arienzo. Tango.info has a list, here.
I syncd. the music with the 1944 Laurenz instrumental version, here. There is some discussion on the form and the use of the rhythms.
The score on Todo Tango has lyrics by José María Contursi, which I haven’t included.
Milonga came before tango and its characteristic rhythm was, and is, the Cuban habanera. Early tango's rhythm was based on the habanera also. Soon other syncopated patterns dominated. The 1st variation, the "syncopa" is the most commonly heard syncopated rhythm in tango music. All three versions are used in milonga.
Habanera Variations describes the syncopation and relationship between these patterns.