We design an observer for ODE-PDE cascades where the ODE is nonlinear of strict-feedback structure and the PDE is a linear and of parabolic type. The observer provides online estimates of the (finite-dimensional) ODE state vector and the (infinite-dimensional) state of the PDE, based only on sampled boundary measurements. A design that simultaneously addresses nonlinear ODEs and boundary measurement sampling is the paper's key contribution. Our observer design combines the backstepping design approach and the high-gain observer methodology and our analysis employs a Lyapunov-Krasovskii type functional to establish exponential convergence. Our sufficient conditions for convergence involve the maximum sampling interval and the PDE domain length. (C) 2018 Elsevier Ltd. All rights reserved.