Boolean Networks (BNs) are a simple formalism used to study complex biological systems when the prediction of exact reaction times is not of interest. They play a key role to understand the dynamics of the studied systems and to predict their disruption in case of complex human diseases. BNs are generally built from experimental data and knowledge from the literature, either manually or with the aid of programs. The automatic synthesis of BNs is still a challenge for which several approaches have been proposed. In this paper, we propose ASKEeD-BN, a new approach based on Answer-Set Programming to synthesise BNs constrained in their structure and dynamics. By applying our method on several well-known biological systems, we provide empirical evidence that our approach can construct BNs in line with the provided constraints. We compare our approach with three existing methods (REVEAL, Best-Fit and caspo-TS) and show that our approach synthesises a small number of BNs which are covering a good proportion of the dynamical constraints, and that the variance of this coverage is low.