Born in Lecco, Stoppani studied theology and became a priest in the order of the Rosminians. He was ordained in 1848, a year of turmoil with the Siege of Milan. During this siege, the Five Days of Milan, he became a hero for his role in the use of hot air balloons to send messages out of the besieged city. Along with Vincenzo Guglielmini, he ensured that the balloons could move over the walls of the city from the Seminario Maggiore di Porta Orientale and carry messages to rally the Italians against the Austrian Empire. He later became professor of geology in the Royal Technical Institute of Milan, and was distinguished for his research on the Triassic and Liassic formations of northern Italy.