The timely establishment of functional neo-vasculature is pivotal for successful tissue development and regeneration, remaining a central challenge in tissue engineering. In this study, we present a novel (micro)vascularization strategy that explores the use of specialized "vascular units" (VUs) as building blocks to initiate blood vessel formation and create perfusable, stroma-embedded 3D microvascular networks from the bottom-up. We demonstrate that VUs composed of endothelial progenitor cells and organ-specific fibroblasts exhibit high angiogenic potential when embedded in fibrin hydrogels. This leads to the formation of VUs-derived capillaries, which fuse with adjacent capillaries to form stable microvascular beds within a supportive, extracellular matrix-rich fibroblastic microenvironment. Using a custom-designed biomimetic fibrin-based vessel-on-chip (VoC), we show that VUs-derived capillaries can inosculate with endothelialized microfluidic channels in the VoC and become perfused. Moreover, VUs can establish capillary bridges between channels, extending the microvascular network throughout the entire device. When VUs and intestinal organoids (IOs) are combined within the VoC, the VUs-derived capillaries and the intestinal fibroblasts progressively reach and envelop the IOs. This promotes the formation of a supportive vascularized stroma around multiple IOs in a single device. These findings underscore the remarkable potential of VUs as building blocks for engineering microvascular networks, with versatile applications spanning from regenerative medicine to advanced models.