We present the novel 2× 4 monolithic Silicon Drift Detectors (SDD) array of 1 mm thickness developed within the context of the SIDDHARTA-2 experiment for high-energy X-ray spectroscopy measurements of light kaonic atom transitions. It represents a state-of-the-art advancement in terms of detection efficiency with respect to the previous generation of detectors, having a thickness of 450 μm. The sensor features eight square SDD units with an active area of 8 × 8 mm2 each, arranged in a 2 × 4 matrix. Therefore, the total active area of the array is 32 × 16 mm2 while the total chip area is 36 × 20 mm2, including a 2-mm dead region on each side of the array. This new version of SDD arrays, manufactured by Fondazione Bruno Kessler (FBK), includes an additional electrode on its entrance window, designed to reduce charge sharing between adjacent channels and improve energy resolution. This article describes two different detection modules based on these arrays: the first module includes a single array, whereas the second one is composed of two 1 mm thick SDD arrays in a stacked configuration, in order to reach 2 mm of effective thickness and further increase the module detection efficiency. The first spectroscopic measurements obtained with the two modules will be also reported in the paper, showing the spectroscopic improvements that can be obtained with the additional electrode on the window and the efficiency improvements that can be obtained with the stacked module.