First of all, we must note that Plessy is not from the Reconstruction era. Reconstruction ended in 1877. Plessy was decided in 1896.
That said, Brown certainly did overturn Plessy. The decision in Plessy held that segregation on trains was legal so long as the accommodations for the two races were “separate but equal.” That logic was applied to all areas of public life. So long as schools were officially equal, it was legal for them to be separate.
The Brown decision threw out this logic, at least for public schools. It held that, in the case of public schools, separate facilities could never truly be equal. This overturned the meat of the doctrine from Plessy.
The ruling was the opposite. In Plessey v. Fergusson "separate but equal" was considered constitutional. Late on Brown v. Board of Ed ruled that "separate but equal" was declared unconstitutional.