After a medical training at the San Matteo hospital in Pavia, Brambilla enrolled as assistant surgeon in the Hagenbach imperial infantry regiment in 1752. He passed the exam for surgeon major at the University of Vienna and, after the Seven Years' War, was appointed in 1763 surgeon of the Noble Bodyguard of Their Imperial Majesties, Maria Theresa (1717-1780) and Francis I (1708-1765) of Habsburg-Lorraine. In 1764, he became personal surgeon to Archduke Joseph (later Emperor Joseph II, 1741-1790). Brambilla achieved fame by promoting the technical and cultural progress of surgery through the establishment of a school at a hospital in a Viennese suburb. The school later became the Academy of Surgery.

To remedy doctors' scant knowledge of the available instruments for performing surgical procedures, Brambilla compiled the Instrumentarium chirurgicum militare Austriacum, published in German in 1780 and in Latin in 1782. This folio volume contains 65 plates with life-size images of the instruments and a text describing every single part. The work inspired three compendia of surgical instruments commissioned by Brambilla - also for teaching purposes. One of these is exhibited at the Museo Galileo of Florence, another at the Institute for the History of Medicine at the University of Vienna, and the third in the Museo dell'Ateneo of Pavia.