Extremely Large-Scale (XL) multiple input multiple output (MIMO) antenna systems combined with ultra-wide signal bandwidth (BW) offer the potential for ultra-high-resolution sensing in frequency modulated continuous wave (FMCW) radars. However, the use of ultra-wide BW results in significant spatial delays across the array aperture, comparable to the range resolution, leading to the spatial wideband effect (SWE). SWE introduces coupling between the range and angle domains, rendering conventional narrowband signal processing techniques ineffective for target signature estimation. In this paper, we propose an efficient super-resolution signature estimation technique for XL-MIMO FMCW radars operating under SWE, leveraging compressive sensing (CS) methods. The proposed 2D CS-based approach offers low computational complexity, making it highly suitable for real-time applications in large-scale radar systems. Numerical simulation results validate the superior performance of the proposed method compared to existing wideband and narrowband estimation techniques.