The aims of this clinical trial are to estimate the efficacy, as well as safety and tolerability of sorafenib, a RAF and tyrosine kinase receptor inhibitor, in the treatment of pediatric patients with recurrent LGA. Sorafenib targets several pathways that, based on preliminary data from us and others, are likely contributing to the growth of LGAs: oncogenic BRAF, which is present in the majority of grade I LGAs and VEGFR2 and PDGFR, which are well-described mediators of tumor angiogenesis. Since sorafenib inhibits a number of additional kinases whose role in LGA growth has not yet been explored, it is possible that inhibition of pathways other than the primary targets may result in additional anti-tumor effects of sorafenib in LGA. Although the investigators hypothesize that LGAs with oncogenic BRAF should be most sensitive to sorafenib, the additional targets of sorafenib may also result in significant anti-tumor effects in LGAs with wild-type BRAF. Therefore, the investigators propose to evaluate the efficacy of sorafenib in children with LGAs in a translational clinical trial, stratified by BRAF status and tumor grade.