The controlled creation and manipulation of defects in 2D materials has become increasingly popular as a means to design and tune new material functionalities. However, defect characterization by direct atomic-scale imaging is often severely limited by surface contamination due to a blanket of hydrocarbons. Thus, analysis techniques that can characterize atomic-scale defects despite the contamination layer are advantageous. In this work, we take inspiration from X-ray absorption spectroscopy and use broad-beam electron energy loss spectroscopy (EELS) to characterize defect structures in 2D hexagonal boron nitride (hBN) based on averaged fine structure in the boron K-edge. Since EELS is performed in a transmission electron microscope (TEM), imaging can be performed in-situ to assess contamination levels and other factors such as tears in the fragile 2D sheets, which can affect the spectroscopic analysis. We demonstrate the TEM-EELS technique for 2D hBN samples irradiated with different ion types and doses, finding spectral signatures indicative of boron-oxygen bonding that can be used as a measure of sample defectiveness depending on the ion beam treatment. We propose that even in cases where surface contamination has been mitigated, the averaging-based TEM-EELS technique can be useful for efficient sample surveys to support atomically resolved EELS experiments.