Broadband precision spectroscopy of rovibrational transitions holds promise for tracking periodic variations in fundamental constants. Such variations may offer evidence supporting the existence of ultralight dark matter and indicate new physics. This talk provides an overview of our efforts in achieving broadband saturation spectroscopy in the mid-infrared. Our focus lies on crystalline super mirrors, featuring a cavity finesse surpassing 400,000, and low-noise high-power frequency combs generating Watt-level output power.