Processing extremely large collections of Earth Observation (EO) time-series, often petabyte-sized, such as NASA's Landsat and ESA's Sentinel missions, can be computationally prohibitive and costly. Despite their name, even the Analysis Ready Data (ARD) versions of such collections can rarely be used as direct input for modeling and require additional time-series processing. Existing solutions for readily using these data are not openly available, are poor in performance, or lack flexibility. Addressing this issue, we developed SIRCLE (Signal Imputation and Refinement with Convolution Leaded Engine), a computational framework that can be used to apply diverse time-series processing techniques by simply adjusting the convolution kernel. Together with SIRCLE, this paper presents SWAG (Seasonally Weighted Average Generalization), a method for EO time-series reconstruction integrated in the framework. SWAG can be used as an imputation method to reconstruct EO images affected by the presence of clouds. Compared to a benchmark dataset, SWAG consistently outperformed the reference methods, reducing reconstruction errors by at least 15%. As the first large-scale application, SIRCLE and SWAG were employed to process the entire Global Land Analysis and Discovery (GLAD) ARD-2 Landsat archive, producing a cloud-free bi-monthly aggregated product. This process, covering seven Landsat bands globally from 1997 to 2022, with more than two trillion pixels and for each one a time-series of 156 samples in the aggregated product, required approximately 28 hours of computation using 1248 Intel(R) Xeon(R) Gold 6248R CPUs. The resulting reconstructed images can be used for machine learning models or to map biophysical indices. With the hosting of about 20 TB per band/index for an entire 30 m resolution, bi-monthly historical time-series, stored as Cloud-Optimized GeoTIFFs (COG) and distributed as open data, the product enables seamless, fast, and affordable access to the Landsat archive for environmental monitoring and analysis applications.