A zonal isolation device conveyed into the wellbore with a propped flapper valve. The zonal isolation device comprises a deformable sealing element and a support ring movably disposed within the inner bore of the sealing element. A flapper valve coupled to the support ring is configured to engage a sealing surface of support ring. The flapper valve blocks fluid flow through the zonal isolation device in a fully closed position, allows unrestricted fluid flow through the zonal isolation device in a fully open position, and allows restricted fluid flow through the zonal isolation device when held by a propping component in an intermediate or partially open position. The zonal isolation device is anchored to the wellbore by an anchoring assembly engaged with a wedge coupled to the downhole end of the sealing element.