The study of how soft particles deform to pass through narrow openings is important for understanding the transit of biological cells, as well as for designing deformable drug delivery carriers. In this work, we systematically explore how soft microparticles with various internal architectures deform during passage through microfluidic constrictions. We synthesize hydrogel particles with well-defined internal structure using lithography-based UV polymerization in microfluidic channels (stop-flow lithography). Using this in situ technique, we explore a range of 2D particle architectures and their effect on particle deformation. We observe that particles undergo buckling of internal supports and reorient at the constriction entrance in order to adopt preferred shapes that correspond to minimum energy configurations. Using finite element simulations of elastic deformation under compression, we accurately predict the optimal deformation configuration of these structured particles.