The bordered Floer homology of a 3-manifold with torus boundary can be interpreted as a collection of immersed curves in the punctured torus. Similarly, the bordered Floer homology of a 3-dimensional cobordism M:T^2->T^2 give an operator F_M which eats an immersed curve on the punctured torus and spits out another such curve. (More formally, F_M is a functor from the Fukaya category of the punctured torus to itself.) I'll describe a class of examples in which these operators are given by explicit geometric correspondences. Based on joint work with Holt Bodish and James Pascaleff.