Ammonia has emerged as a promising carbon-free fuel for mitigating greenhouse gas emissions. However, its application in practical combustion systems is limited by several issues including its low heating value and slow flame propagation speed, which have posed challenges in maintaining stable combustion. As an attempt to resolve these issues, we numerically investigated premixed ammonia–air combustion using a detailed chemical mechanism in a heat-recirculating, Swiss-roll burner that was proposed based on the concept of “excess-enthalpy.” The main focus was put on the flame stabilizations as well as characteristics of NO/N2O emissions across a wide range of operational conditions. The results showed that the use of the Swiss-roll burner led to a significantly broadened stability regime for pure ammonia combustion, which could be attributed to the effective preheating from combustion products to unburnt mixture. The relationship between the dimensionless heat transfer parameter and excess-enthalpy was quantified and a linear correlation was revealed. In addition, flow expansion and recirculation within the combustion chamber led to the generation of vortices, which was also beneficial for flame stabilizations. NO emissions at the burner outlet were witnessed to have a linear growth in the laminar flow region, a gentler increase in the flow-transition stage, and a final leveling off at the turbulent flow condition with the increase in Reynolds number. For a given Reynolds number, the NO emission showed a non-monotonic variation with equivalence ratios, with relatively low emission levels at either the fuel-lean or fuel-rich conditions. As another major concern, N2O emission was found more significant in the laminar flow region and at fuel-lean conditions, both of which should be avoided in practical operations.