He completed a mason's apprenticeship under court mason Johan Heinrich Brandemann and was then admitted to the Royal Danish Academy of Fine Arts where he won the small silver medal in 1789 and the large silver medal in 1789.
Schønberg Kurtzhals was established as a master mason in 1796 and profited from the enormous need for construction services that had followed from the extensive destruction caused by the Great Fire of 1795 the previous year.
Schønberg Kurtzhals was a friend of Bertel Thorvaldsen during his student years at the academy.
His sister Sophie Amalie Kurtzhals and Thorvaldsen were sweethearts before he left for Rome in 1796.
On his departure, he gave her an allegorical drawing titled Time Rewards Virtue but eventually she grew tired of waiting and married master mason Johann Joachim Schlage.