Common Randomness (CR) provides sequences of random variables at two physically separated locations. Ideally, the random variables at the two locations should be identical, i.e., have low probability of discrepancy, and should have high entropy. Previous CR research has focused on CR for physical layer security (mainly physical layer secret key generation), where a low CR generation rate, i.e., a low rate of CR bits per second is sufficient. However, emerging semantic communication paradigms, e.g., identification via channels, require high CR rates. We develop and evaluate a Carrier Frequency Offset (CFO) based methodology for high-rate CR generation from reciprocal observations of a common wireless channel between two distinct wireless terminals. The proposed CFO-CR methodology proceeds in several stages, including channel probing, random parameter extraction, noise reduction, quantization, information reconciliation, and randomization. Our evaluations with single-carrier software-defined radios, for which we make measurement traces publicly available, indicate that high-rate CR generation should observe (probe) the CFO and employ a Savitzky Golay low-pass filter with a low cut-off frequency for noise reduction in conjunction with multi-bit quantization, Gray code encoding, and a shuffling based randomization. We provide insights into the tradeoffs between the reconciliation cost for correcting bit discrepancies and the CR generation parameters. Our proposed CFO-CR methodology can generate 2048 bits of CR at a comparatively low reconciliation cost of 72 bytes while only making 256 channel observations and passing all common randomness tests. For generating 2048 bits of CR, other state-of-the-art approaches either require more channel observations (≥ 2048 ) or incur a higher reconciliation cost (≥ 450 bytes).