In a Gray-Box Optimization (GBO) setting that allows for partial evaluations, the fitness of an individual can be updated efficiently after a subset of its variables has been modified. This enables more efficient evolutionary optimization with the Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) due to its key strength: Gene-pool Optimal Mixing (GOM). For each solution, GOM performs variation for many (small) sets of variables. To improve efficiency even further, parallel computing can be leveraged. For EAs, typically, this comprises population-wise parallelization. However, unless population sizes are large, this offers limited gains. For large GBO problems, parallelizing GOM-based variation holds greater speed-up potential, regardless of population size. However, this potential cannot be directly exploited because of dependencies between variables. We show how graph coloring can be used to group sets of variables that can undergo variation in parallel without violating dependencies. We test the performance of a CUDA implementation of parallel GOM on a Graphics Processing Unit (GPU) for the Max-Cut problem, a well-known problem for which the dependency structure can be controlled. We find that, for sufficiently large graphs with limited connectivity, finding high-quality solutions can be achieved up to 100 times faster, showcasing the great potential of our approach.