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Controlling the flow of broadband electromagnetic energy at the nanoscale remains a critical challenge in optoelectronics. Surface plasmon polaritons (or plasmons) provide subwavelength localization of light, but are affected by significant losses. On the contrary, dielectrics lack a sufficiently robust response in the visible to trap photons similar to metallic structures. Overcoming these limitations appears elusive, as it implies devising a path to circumvent causality in the quantum-mechanical form of matter. Here we demonstrate that addressing this problem is possible if we employ a novel approach based on suitably deformed reflective metaphotonic structures. The complex geometrical shape engineered in these reflectors emulates nondispersive index responses, which can be inverse-designed following arbitrary form factors. We discuss the realization of essential components such as resonators with an ultra-high refractive index of $n=100$ in diverse profiles. These structures support localization of light in the form of bound states in the continuum (BIC), fully localized in air, in a platform in which all refractive index regions are physically accessible. We discuss our approach to sensing applications, designing a class of sensors where the analyte directly contacts areas of ultra-high refractive index. Leveraging this feature, we report differential sensitivities up to $350$~nm/RIU in structures with footprints of approximately one micron. These performances are two times better than the closest competitor with a similar form factor. Inversely designed reflective metaphotonics offers a flexible technology for controlling broadband light, supporting optoelectronics' integration with large bandwidths in circuitry with miniaturized footprints.