In this work, we present a novel isogeometric topology optimization method tailored for complex design domains represented by boundary representations (B-reps). The topology optimization is reformulated as a generalized Cahn-Hilliard problem in which sensitivity analysis is not needed. The optimized structure is then found by finding the steady-state solution of the time-dependent, high-order nonlinear partial differential equation, which is solved on a cut Cartesian grid by the B-rep. To address the instability issue caused by small cut elements, we employ the minimal stabilization method in the nonlinear setting with the Nitsche’s formulation. Numerical integration is handled by folded decomposition where negative Jacobian is allowed for the integration purpose only. Through several numerical examples, we demonstrate the efficacy and robustness of the proposed method in handling complex design domains.