This work presents a numerical study of the acoustic response of a laminar flame with tunable asymmetry. A V-shaped premixed flame is stabilised in the wake of a cylindrical flame holder that can be rotated. The configuration is symmetric when the flame holder is fixed but increasing its rotation rate breaks the symmetry of the flow. This configuration is submitted to acoustic forcing to measure the effect of rotation of the flame holder on the Flame Transfer Functions. It appears that the asymmetry of the two flame branches changes their respective time delays, resulting in interference in the global unsteady heat release rate fluctuations. Consequently, the Flame Transfer Function exhibits dips and bumps, which are studied via laminar Direct Numerical Simulation. Potential applications for the control of combustion instabilities are discussed.