A major goal of HIV-1 vaccine development is the induction of broadly neutralizing antibodies (bnAbs). Although success has been achieved in initiating bnAb B cell lineages, design of boosting immunogens that select for bnAb B cell receptors with improbable mutations required for bnAb affinity maturation remains difficult. Here, we demonstrate a process for designing boosting immunogens for a V3-glycan bnAb B cell lineage. The immunogens induced affinity-matured antibodies by selecting for functional improbable mutations in bnAb precursor knockin mice. Moreover, we show similar success in prime and boosting with nucleoside-modified mRNA-encoded HIV-1 envelope trimer immunogens, with improved selection by mRNA immunogens of improbable mutations required for bnAb binding to key envelope glycans. These results demonstrate the ability of both protein and mRNA prime-boost immunogens for selection of rare B cell lineage intermediates with neutralizing breadth after bnAb precursor expansion, a key proof of concept and milestone toward development of an HIV-1 vaccine. Display omitted •HIV vaccine immunogen design process to select for improbable antibody (Ab) mutations•Just 4 improbable mutations needed to elicit V3 glycan broadly neutralizing Ab (bnAb)•Prime/boosting of unmutated V3 glycan bnAb knockin mice elicits maturation of bnAbs•mRNA-LNP immunogens are superior for selecting key glycan-contacting improbable mutations Wiehe et al. describe a vaccine design strategy for developing boosting immunogens for guiding the development of HIV-1 broadly neutralizing antibodies (bnAbs) based on identifying and selecting improbable antibody mutations. Using this strategy, bnAb precursor knockin mice immunized with a designed boosting immunogen elicited bnAbs with key improbable mutations.