We present a novel geometry of microfluidic channels that allows us to passively generate monodisperse emulsions of hundreds of droplets smaller than 1 nL from collections of larger (ca. 0.4 μL) mother droplets. We introduce a new microfluidic module for the generation of droplets via passive break-up at a step. The module alleviates a common problem in step emulsification with efficient removal of the droplets from the vicinity of the step. In our solution, the droplets are pushed away from the step by a continuous liquid that bypasses the mother droplets via specially engineered bypasses that lead to the step around the main channel. We show that the bypasses tighten the distribution of volume of daughter droplets and eliminate subpopulations of daughter droplets. Clearing away the just produced droplets from the vicinity of the step provides for similar conditions of break-up for every subsequent droplet and, consequently, leads to superior monodispersity of the generated emulsions. Importantly, this function is realized autonomously (passively) in a protocol in which only a sequence of large mother droplets is forced through the module. Our system features the advantage of step emulsification systems in that the volumes of the generated droplets depend very weakly on the rate of flow through the module - an increase in the flow rate by 300% causes only a slight increase of the average diameter of generated droplets by less than 5%. We combined our geometry with a simple T-junction and a simple trap-based microdroplet dilutor to produce a collection of libraries of droplets of gradually changing and known concentrations of a sample. The microfluidic system can be operated with only two syringe pumps set at constant rates of flow during the experiment.