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Recent years have seen the development of quantum sensing concepts utilizing nonlinear interferometers based on correlated photon pairs generated by spontaneous parametric down-conversion (SPDC). Using SPDC far from frequency degeneracy allows a "division of labor" between the mid-infrared photon for the strongest sample interaction and the correlated near-infrared photon for low-noise detection. The small number of photons provided by SPDC and the resulting inferior signal-to-noise ratio are, however, a limiting factor preventing the wide applicability of the novel sensing concept. Here, we demonstrate a nonlinear interferometer based on pump-enhanced SPDC with strongly improved emission rates while maintaining broadband spontaneous emission. For validation of the concept, we demonstrate high-resolution mid-infrared spectroscopy with near-infrared detection, showcasing improved accuracy. Although the number of mid-infrared photons is about five orders of magnitude smaller than in classical spectrometers, the sensitivity of the quantum spectrometer becomes comparable, marking an essential step toward real-world applications. [ABSTRACT FROM AUTHOR]