Laser Powder Bed Fusion (LPBF) stations mostly use lasers with a Gaussian beam intensity distribution, as it has advantages like small divergence and high ability to be focused. This distribution creates significant thermal gradients leading to high cooling rates, which promote the formation of an alpha'-martensitic structure in Ti-6Al-4V. While this microstructure offers high strength, it sacrifices ductility, necessitating post-processing heat treatments to decompose the alpha'-martensite into an alpha+beta lamellar structure. However, these post-treatments are time-consuming, and notably transform the part microstructure in a uniform way. In this study, an advanced laser beam shaping module, based on a liquid crystals on silicon-spatial light modulator (LCoS-SLM) is employed, to customize the intensity distribution and reduce the cooling rate with appropriate processing parameters. Thermal camera monitoring, along with finite element modeling (FEM), confirmed a significant reduction in the cooling rate for the tailored beam, compared to the Gaussian profile. This technique is implemented in the LPBF process, resulting in specimens with a mixture of lamellar alpha+beta and alpha'-martensitic structures site specifically. Beam shaping is thereby shown to provide new degrees of freedom for fine-tuning of microstructures at the melt pool scale, and for LPBF building of 3D architected microstructures.