Closed string field theory is governed by an L-infinity algebra of interactions, with quantum action satisfying BV-master equation. We will describe a B-twisted version of topological closed string field theory. As an example, we explain a complete solution of quantum BV-master equation on elliptic curves in terms of chiral algebras via an evolution of integrable system and its relation with quasi-modular forms. This leads to a simple description of the corresponding higher genus mirror symmetry.