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This study presents a meteorologically-based methodology for quantifying basin-scale methane (CH4) emissions in Utah's Uintah Basin, which is home to over 9,000 active and producing oil and natural gas wells. Previous studies in oil and gas producing regions have often relied on intensive aircraft campaigns to estimate methane emissions. However, the high cost of airborne campaigns prevents their frequent undertaking, thus providing only daytime snapshots of emissions rather than more temporally-representative estimates over multiple days. Providing estimates of CH4 emissions from oil and natural gas production regions across the United States is important to inform leakage rates and emission mitigation efforts in order to curb the potential impacts of these emissions on global climate change and local air quality assessments. Here we introduce the Basin-constrained Emissions Estimate (BEE) method, which utilizes the confining topography of a basin and known depth of a pollution layer during multi-day wintertime cold-air pool episodes to relate point observations of CH4 to basin-scale CH4 emission rates. This study utilizes ground-based CH4 observations from three fixed sites to calculate daily increases in CH4, a laser ceilometer to estimate pollution layer depth, and a Lagrangian transport model to assess the spatial representativity of surface observations. BEE was applied to two cold-air pool episodes during the winter of 2015-2016 and yielded CH4 emission estimates between 44.60 +/- 9.66 x 10(3) and 61.82 +/- 19.76 x 10(3) kg CH4 hr(-1), which are similar to the estimates proposed by previous studies performed in the Uintah Basin. The techniques used in this study could potentially be utilized in other deep basins worldwide.