The Neutron star Interior Composition Explorer (NICER) X-ray observatory observed two powerful X-ray flares equivalent to superflares from the nearby young solar-like star κ 1 Ceti in 2019. NICER follows each flare from the onset through the early decay, collecting over 30 counts s−1 near the peak, enabling a detailed spectral variation study of the flare rise. The flare in September varies quickly in ∼800 s, while the flare in December has a few times longer timescale. In both flares, the hard-band (2–4 keV) light curves show typical stellar X-ray flare variations with a rapid rise and slow decay, while the soft X-ray light curves, especially of the September flare, have prolonged flat peaks. The time-resolved spectra require two temperature plasma components at kT ∼0.3–1 and ∼2–4 keV. Both components vary similarly, but the cool component lags by ∼200 s with a four to six times smaller emission measure (EM) compared to the hot component. A comparison with hydrodynamic flare loop simulations indicates that the cool component originates from X-ray plasma near the magnetic loop footpoints that mainly cools via thermal conduction. The time lag represents the travel time of the evaporated gas through the entire flare loop. The cool component has a several times smaller EM than its simulated counterpart, suggesting a suppression of conductive cooling, possibly by the expansion of the loop cross-sectional area or turbulent fluctuations. The cool component’s time lag and EM ratio provide important constraints on the flare loop geometry.