Conventional processing tools of glass cannot fulfil the forever increasing industrial requirements for processing speed and quality. In the future these methods can be replaced by emerging laser-based techniques. While nowadays most of the research is dedicated for thin, especially chemically strengthened glass, used in electronic devices, there is still a need for a suitable processing technique for thick glasses. One of the most material-efficient and energy-efficient glass cutting techniques is to locally weaken the material along the cutting path by generating cracks or material modifications and then separate sheets by applying thermal or mechanical load. Such approach provides a clean cut with an infinitely thin kerf width without a need for post-processing. Bessel-Gaussian beams, commonly generated using a conical lens, have very appealing properties for processing of transparent materials, such as the long non-diffractive propagation length and self-reconstruction. However, due to manufacturing tolerances, the shape of an optical element deviates from an ideal cone and the intensity pattern is non-symmetrical and modulated along the beam propagation axis. We have found that such asymmetry leads to the significant elongation of laser-induced glass cracks along one dominant direction, which can be beneficial for fast glass cutting.