We develop an exact spectral-response theory for the Grover-type iterate (W_T=D_(- T H)), in which the evolution generated by a diagonal Ising Hamiltonian is used directly as a continuous phase oracle. An energy-grouped recurrence and its generating-function solution show how the empirical characteristic function determines the position, width, height, and saturation time of an energy-selective resonance. For an annealed Gaussian density of states, a high-density-tail resonance containing (M) configurations is reached after (()) oracle calls with success probability ((1)), giving a quadratic query improvement over independent uniform sampling with classical energy evaluation. For correlated random Ising spectra, overlap-dependent covariances lead to a realization-dependent resonance shift with root-mean-square scale (O(n^{-3})), parametrically larger than the resonance width, and can also reduce the peak height. The shift is both an algorithmic detuning and a coherent probe of sample-specific spectral fluctuations whose ensemble statistics reflect the Ising overlap structure. Spectral symmetrization and iterative calibration can remove or compensate the resonance-center displacement for prescribed-energy targeting. We also clarify the relation to designed spectral filters and the precision and coherence requirements of this asymptotic primitive.