Fronthaul limitations in terms of capacity and latency motivate the growing interest in the wireless industry for the study of alternative functional splits between cloud and edge nodes in Cloud Radio Access Network (C-RAN). This work contributes to this line of work by investigating the optimal functional split of control and data plane functionalities at the edge nodes and at the Remote Cloud Center (RCC) as a function of the fronthaul latency. The model under study consists of a two-user time-varying uplink channel in which the RCC has global but delayed channel state information (CSI) due to fronthaul latency, while edge nodes have local but timely CSI. Adopting the adaptive sum-rate as the performance criterion, functional splits whereby the control functionality of rate selection and the decoding of the data-plane frames are carried out at either the edge nodes or at the RCC are compared through analysis and numerical results.