Parschau was born in Klausen , in the Allenstein district of East Prussia. He became a commissioned officer a year after having joined the Infanterie-Regiment Nr. 151 in 1910. Parschau was trained as a pilot in Johannisthal, Darmstadt, and in Hanover and received his licence on 4 July 1913.
Parschau was assigned the Fokker A.III aircraft bearing both the Fokker factory serial number216 and the IdFlieg military serial number of A.16/15. This airplane had previously been flown by Oberleutnant . This unarmed monoplane had been privately purchased in 1913 by von Buttlar. It was requisitioned by the Fliegertruppe and von Buttlar was commissioned as an officer in the German Army at the outbreak of hostilities. The airplane was painted in a shade of green that was the same as that used by von Buttlar's previous Marburg-based Jäger Regiment 11. Parschau had served with the same, Brieftauben-Abteilung Ostende unit, abbreviated as BAO in German military communications of the time, in Belgium as Oberleutnant von Buttlar did in November 1914, where the two German officers could have first made contact. As A.16/15 still bore the green color of von Buttlar's old unit, the aircraft became distinctive as Parschau's 'Green Machine', right from the outbreak of World War I. Parschau flew this machine on a roving commission for nearly a year, serving with FFAs 22 and 42 and the aforementioned , which was actually a group of four FFA units operating as one for the Oberste Heeresleitung or OHL, the World War I German Army's High Command office. In this period, Parschau flew his distinctive machine on the Champagne front during October and November 1914. Following this were periods in Flanders and Alsace-Lorraine before Parschau was posted first to West Prussia and then on to Galicia on the Eastern Front. His travels were marked on the Fokker's fuselage. In late May 1915, this airplane was the first one to be fitted with a workable synchronization gear: the Fokker Stangensteuerung synchronizer, along with a Parabellum MG 14 machine gun for its armament. This airplane functioned as the prototype Fokker Eindecker for Parschau's use and combat evaluation. ever produced, shown with "lowered" wing mount location.
Later war service
Because Parschau was recognised as an experienced and proficient pilot, he was selected to go to Feldflieger Abteilung 62 at Douai as an instructor on monoplanes. Feldflieger Abteilung was the title of the pioneering German field aviation units. The FFAs were organized under the Fliegertruppe. By October 1916, the Fliegertruppe had evolved into the Luftstreitkräfte, the air service of the German army. Amongst Parschau's students at FFA 62 were the notable pioneer German flying aces, Max Immelmann and Oswald Boelcke. Despite his earlier complaints of his Parabellum machine gun jamming, he managed to reel off a string of six victories over enemy airplanes between 11 October 1915 and 2 July 1916 as part of the Fokker Scourge. On 3 July 1916, he shot down an enemy observation balloon. In July 1916 he transferred to FFA 32, gaining his 8th victory on 9 July 1916. He was awarded the Pour le Merite the following day. On the 14th, AKN was severed from FFA 32 and Parschau was appointed to its command. On 21 July 1916 Parschau was mortally wounded during combat with the Royal Flying Corps over Grévillers. The fatal wound was to the chest, he also suffered a glancing bullet wound to the head, possibly from rounds fired by John Oliver Andrews. He retained enough control to land his plane behind German lines. He was rushed to a field hospital but died on the operating table.