As quantum platforms scale up, the accurate and efficient design of parallel quantum gates is increasingly hindered by unwanted interaction terms between driven and spectator qubits, commonly referred to as crosstalk. Accounting for these effects typically requires a full-system optimization, whose computational cost grows exponentially with system size. Here, we overcome this challenge by recasting the optimization as a crosstalk-robust problem defined on polynomial-sized pairs of subsystems, dramatically reducing the required computational resources. Within this framework, we construct analytical pulses for parallel single-qubit gates and numerical pulses for parallel multiqubit gates. We numerically validate the framework on Ising chains and nuclear-spin processors, and further assess its scalability by demonstrating the effectiveness of the resulting robust controls on subsystem blocks of superconducting qubit arrays containing up to 200 qubits. Our approach does not require precise calibration of the crosstalk interaction strengths and applies to arbitrary qubit connectivity, providing an efficient route toward scalable design of parallel quantum gates for large-scale quantum processors.