The Kepler mission has provided a treasure trove of eclipsing binaries (EBs), observed at extremely high photometric precision, nearly continuously for several years. We are carrying out a survey of ~100 of these EBs to derive dynamical masses and radii with precisions of 3% or better. We use multiplexed near-infrared H-band spectroscopy from the Sloan Digital Sky Survey-III and -IV APOGEE instrument and optical spectroscopy from the Hobby–Eberly Telescope High-resolution Spectrograph to derive double-lined spectroscopic orbits and dynamical mass ratios (q) for the EB sample, two of which we showcase in this paper. This orbital information is combined with Kepler photometry to derive orbital inclination, dynamical masses of the system components, radii, and temperatures. These measurements are directly applicable for benchmarking stellar models that are integrating the next generation of improvements, such as the magnetic suppression of convection efficiency, updated opacity tables, and fine-tuned equations of state. We selected our EB sample to include systems with low-mass (M ≾
0.8 M⊙) primary or secondary components, as well as many EBs expected to populate the relatively sparse parameter space below ~0.5 M⊙. In this paper, we describe our EB sample and the analytical techniques we are utilizing, and also present masses and radii for two systems that inhabit particularly underpopulated regions of mass–radius–period space: KIC 2445134 and KIC 3003991. Our joint spectroscopic and photometric analysis of KIC 2445134 (q = 0.411 ± 0.001) yields masses and radii of M_A = 1.29 ± 0.03 M⊙, M_B = 0.53 ± 0.01 M⊙, R_A = 1.42 ± 0.01 R⊙, R_B = 0.510 ± 0.004 R⊙, and a temperature ratio of T_B/T_A = 0.635 ± 0.001; our analysis of KIC 3003991 (q = 0.298 ± 0.006) yields M_A = 0.74 ± 0.04 M⊙, M_B = 0.222 ± 0.007 M⊙, R_A = 0.84 ± 0.01 R⊙, R_B = 0.250 ± 0.004 R⊙, and a temperature ratio of T_B/T_A = 0.662 ± 0.001
