Aims. In single-lens microlensing events, the event timescale (tE) is typically the only measurable parameter that constrains the lens mass. Since tE scales with the square root of the lens mass (tE ∝ M1/2), a short duration may suggest a low-mass lens, such as a brown dwarf (BD). However, a short tE can also result from a high relative proper motion between the lens and the source, making it difficult to uniquely identify BD candidates based on timescale alone. In contrast, binary-lens events often allow for the measurement of the angular Einstein radius (θE) in addition to tE. When both tE and θE are small, the likelihood that the lens is of low mass increases significantly. In this study, we analyze microlensing events observed between 2023 and 2024 to identify cases likely caused by binary systems composed of BDs. Methods. Applying the criteria of well-resolved caustics, short timescales (tE ≲ 9 days), and small angular Einstein radii (θE ≲ 0.17 mas), we identified six candidate binary BD events: MOA-2023-BLG-331, KMT-2023-BLG-2019, KMT-2024-BLG-1005, KMT-2024-BLG-1518, MOA-2024-BLG-181, and KMT-2024-BLG-2486. Analysis of these events leads to models that provide precise estimates for both lensing observables, tE and θE. Results. We estimated the masses of the binary components through Bayesian analysis, utilizing the constraints from tE and θE. The results show that for the events KMT-2024-BLG-1005, KMT-2024-BLG-1518, MOA-2024-BLG-181, and KMT-2024-BLG-2486, the probability that both binary components lie within the BD mass range exceeds 50%, indicating a high likelihood that the lenses of these events are binary BDs. In contrast, for MOA-2023-BLG-331L and KMT-2023-BLG-2019L, the probabilities that the lower-mass components of the binary lenses lie within the BD mass range exceed 50%, while the probabilities for the heavier components are below 50%, suggesting that these systems are more likely to consist of a low-mass M dwarf and a BD. The BD nature of the binary candidates can ultimately be confirmed by combining the measured lens-source relative proper motions with high-resolution imaging taken at a later time.