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Stochastic systems that undergo random restarts to their initial state have been widely investigated in recent years, both theoretically and in experiments. Oftentimes, however, resetting to a fixed state is impossible due to thermal noise or other limitations. As a result, the system configuration after a resetting event is random. Here, we consider such a resetting protocol for an overdamped Brownian particle in a confining potential V(x). We assume that the position of the particle is reset at a constant rate to a random location x, drawn from a distribution p_{R}(x). To investigate the thermodynamic cost of resetting, we study the stochastic entropy production S_{Total}. We derive a general expression for the average entropy production for any V(x), and the full distribution P(S_{Total}|t) of the entropy production for V(x)=0. At late times, we show that this distribution assumes the large-deviation form P(S_{Total}|t)∼exp{−t^{2α−1}ϕ[(S_{Total}−〈S_{Total}〉)/t^{α}]}, with 1/2<α≤1. We compute the rate function ϕ(z) and the exponent α for exponential and Gaussian resetting distributions p_{R}(x). In the latter case, we find the anomalous exponent α=2/3 and show that ϕ(z) has a first-order singularity at a critical value of z, corresponding to a real-space condensation transition.