Turbulent breaking waves entrain air cavities that break up and coalesce to form polydisperse clouds of bubbles. We recently provided theoretical and numerical justification that the dominant mechanism for super-Hinze-scale bubble generation is a fragmentation cascade from large to small sizes sustained by turbulent velocity fluctuations. This behavior should be universal across various turbulent bubbly flows because of the size locality inherent in a cascade. Universality simplifies the development of subgrid-scale (SGS) breakup models in two-phase large eddy simulations (LES). We formulate an SGS breakup model based on a breakup cascade in accordance with the LES paradigm, where large bubbles are resolved through a two-phase Eulerian description, while small bubbles are separately modeled and tracked as Lagrangian point particles. This model requires the generation and breakup of Lagrangian particles from underresolved Eulerian bubbles with suitable distributions for breakup rates and child bubble sizes. A priori testing and a posteriori implementation of the model in a coarse breaking-wave simulation are discussed, and the need for an accurate modeled breakup mass flux between sizes is underscored. Relations to the dynamic model in single-phase turbulence simulations are also explored, with direct analogy to the central role of the turbulent kinetic energy interscale flux in the single-phase model.