We present a novel technique for studying the quenching of shell gaps in exotic isotopes. The method is based on extracting Gamow-Teller (ΔL=0, ΔS=1) transition strengths [B(GT)] to low-lying states from charge-exchange reactions at intermediate beam energies. These Gamow-Teller strengths are very sensitive to configuration mixing between cross-shell orbitals, and this technique thus provides an important complement to other tools currently used to study cross-shell mixing. This work focuses on the N=8 shell gap. We populated the ground and 2.24 MeV 0 + states in Be12 using the B12(1 +) (Li7, Be7) reaction at 80MeV/u in inverse kinematics. Using the ground-state B(GT) value from β-decay measurements (0.184±0.007) as a calibration, the B(GT) for the transition to the second 0 + state was determined to be 0.214±0.051. Comparing the extracted Gamow-Teller strengths with shell-model calculations, it was determined that the wave functions of the first and second 0 + states in Be12 are composed of 25±5% and 60±5% (0s)4 (0p)8 configurations, respectively.