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We consider a continuous time simple random walk on a subset of the squareÌýlattice with wired boundary conditions: The walk transitions at unit edgeÌýrate on the graph obtained from the lattice closure of the subset byÌýcontracting the boundary into one vertex. We study the cover time of suchÌýwalk, namely the time it takes for the walk to visit all vertices in theÌýgraph. Taking a sequence of subsets obtained as scaled lattice versions of aÌýnice planar domain, we show that the square root of the cover timeÌýnormalized by the size of the subset, is tight around $\frac{1}{\sqrt{\pi}}\log N - \frac{1}{4 \sqrt{\pi}} \log \log N$, where $N$ is the scaleÌýparameter. The proof is based on comparison with the extremal landscape ofÌýthe discrete Gaussian free field. Joint work with Marek Biskup and SantiagoÌýSaglietti.