We present an application of quantile generalised additive models (QGAMs) to study spatially compounding climate extremes, namely extremes that occur (near-) simultaneously in geographically remote regions. We take as an example wintertime cold spells in North America and co-occurring wet or windy extremes in Western Europe, which we collectively term Pan-Atlantic compound extremes. QGAMS are largely novel in climate science applications and present a number of key advantages over conventional statistical models of weather extremes. Specifically, they remove the need for a direct identification and parametrisation of the extremes themselves, since they model all quantiles of the distributions of interest. They thus make use of all information available, and not only of a small number of extreme values. Moreover, they do not require any a priori knowledge of the functional relationship between the predictors and the dependent variable. Here, we use QGAMs to both characterise the co-occurrence statistics and investigate the role of possible dynamical drivers of the Pan-Atlantic compound extremes. We find that cold spells in North America are a useful predictor of subsequent wet or windy extremes in Western Europe, and that QGAMs can predict those extremes more accurately than conventional peak-over-threshold models.