The quantum Mpemba effect is a non-equilibrium phenomenon where the restoration of a broken symmetry occurs more rapidly when the initial state exhibits a higher degree of symmetry breaking. This effect has been observed in one-dimensional systems and is now studied in two-dimensional free-fermion systems using entanglement asymmetry as a measure of symmetry breaking. The study focuses on a system with nearest-neighbor hoppings and superconducting pairings, which explicitly breaks the $ U(1) $ particle number symmetry. The entanglement asymmetry is calculated using dimensional reduction, allowing for a smooth crossover between one and two dimensions. After a quench to a Hamiltonian with only nearest-neighbor hoppings, the entanglement asymmetry is studied to determine the conditions under which the quantum Mpemba effect occurs. The effect is strongly influenced by the size of the system in the transverse direction, with the potential to either enhance or spoil the phenomenon depending on the initial states. The conditions for the quantum Mpemba effect are determined based on the properties of the initial configurations, extending the criteria found in one-dimensional systems. The study shows that the quantum Mpemba effect can occur in two-dimensional systems, with the effect being robust when the transverse dimension is increased. The results demonstrate that the quantum Mpemba effect is a complex phenomenon that depends on the initial states and the system geometry.The quantum Mpemba effect is a non-equilibrium phenomenon where the restoration of a broken symmetry occurs more rapidly when the initial state exhibits a higher degree of symmetry breaking. This effect has been observed in one-dimensional systems and is now studied in two-dimensional free-fermion systems using entanglement asymmetry as a measure of symmetry breaking. The study focuses on a system with nearest-neighbor hoppings and superconducting pairings, which explicitly breaks the $ U(1) $ particle number symmetry. The entanglement asymmetry is calculated using dimensional reduction, allowing for a smooth crossover between one and two dimensions. After a quench to a Hamiltonian with only nearest-neighbor hoppings, the entanglement asymmetry is studied to determine the conditions under which the quantum Mpemba effect occurs. The effect is strongly influenced by the size of the system in the transverse direction, with the potential to either enhance or spoil the phenomenon depending on the initial states. The conditions for the quantum Mpemba effect are determined based on the properties of the initial configurations, extending the criteria found in one-dimensional systems. The study shows that the quantum Mpemba effect can occur in two-dimensional systems, with the effect being robust when the transverse dimension is increased. The results demonstrate that the quantum Mpemba effect is a complex phenomenon that depends on the initial states and the system geometry.