This work proposes a numerical framework for mean-field control (MFC) problems based on an adjoint-driven optimization procedure motivated by the stochastic maximum principle (SMP). Rather than globally approximating the adjoint processes $(Y_t,Z_t)$  as functions of the state and the population distribution, we construct sample-wise, conditionally unbiased estimators of their time-discretized counterparts and use these estimators directly to form sample-wise approximations of the Hamiltonian control gradient. The resulting control labels are then regressed to reconstruct the feedback control, which is updated iteratively through a gradient-descent scheme. In this way, the adjoint variables are used only sample-wise and are never learned as global functions. The proposed approach differs from many direct deep-learning methods, which follow a discretize-then-optimize paradigm by parameterizing the control globally and differentiating the fully discretized objective through the simulated state dynamics. For the standard stochastic optimal control problem without mean-field interactions, we further relate our framework to Basic Adjoint Matching (BAM) and Lean Adjoint Matching, clarifying both their common adjoint structure and the differences in how the adjoint information is represented and computed. Numerical experiments demonstrate competitive performance relative to direct deep-learning approaches, with improved accuracy or computational efficiency on several tested problems. The sample-wise and regression-based structure is particularly amenable to high-dimensional particle implementations and to generative modeling problems involving distributional objectives.