This is a Phase I study to evaluate the safety profile of a type of immune therapy called HER2 CAR T cells (short for HER2 chimeric antigen receptor T cells). In addition to looking for side effects, we will study how well this treatment works against a brain tumor called ependymoma that has come back after treatment (recurrent) or has not responded well to treatment (progressive) in children. The HER2 CAR T cells used in this trial are made from the patient's own blood. A new gene, called the HER2 CAR, will be inserted into patient's T cells to allow them recognize a protein on the tumor called HER2. These HER2-specific CAR T cells may be able to target and kill ependymoma tumors that express HER2. This research is also studying how doable it is to provide this type of CAR T cell treatment to children being treated at different hospitals.