Epithelial organoids are stem cell-derived tissues that approximate aspects of real organs, and thus they have potential as powerful tools in basic and translational research. By definition, they self-organize, but the structures formed are often heterogeneous and irreproducible, which limits their use in the lab and clinic. We describe methodologies for spatially and temporally controlling organoid formation, thereby rendering a stochastic process more deterministic. Bioengineered stem cell microenvironments are used to specify the initial geometry of intestinal organoids, which in turn controls their patterning and crypt formation. We leveraged the reproducibility and predictability of the culture to identify the underlying mechanisms of epithelial patterning, which may contribute to reinforcing intestinal regionalization in vivo. By controlling organoid culture, we demonstrate how these structures can be used to answer questions not readily addressable with the standard, more variable, organoid models.