  Dimer models provide a method of constructing noncommutative crepant
resolutions of affine toric Gorenstein threefolds. In homological mirror
symmetry, they can also be used to describe noncommutative Landau--Ginzburg
models dual to punctured Riemann surfaces. For a zigzag consistent dimer
embedded in a torus, we explicitly compute the Hochschild cohomology of its
Jacobi algebra in terms of dimer combinatorics. This includes a full
characterization of the Batalin--Vilkovisky structure induced by the
Calabi--Yau structure of the Jacobi algebra. We then compute the compactly
supported Hochschild cohomology of the category of matrix factorizations for
the Jacobi algebra with its canonical potential.
