This work proposes a pragmatic method for the design of beam footprint layouts and beam hopping illumination patterns to efficiently broadcast 3GPP NTN common signaling to large coverage areas using EIRP-limited LEO satellites. This method minimizes the time resources required to sweep over the whole coverage while ensuring that the signal-to-interference-plus-noise ratio received by users is above a given threshold. It discusses the design of: (i) an Earth-fixed grid of beam layouts; (ii) beamforming vectors and beam power allocation; (iii) beam hopping patterns and (iv) space, time and frequency resource allocation of 3GPP common signaling. Two main beam layout solutions are proposed to significantly reduce the number of beams required to illuminate the coverage area: one based on phased array beams with low beam crossover levels and the other on widened beams. A numerical evaluation using practical system parameters showed that both solutions perform similarly, but that the best result is obtained with phased arrays beams with optimized beam cross over levels. Indeed, for the system evaluated, they allowed reducing the total number of beams from 1723 to 451, which combined with a proper beam hopping pattern and scheduling scheme allowed obtaining a coverage ratio of 100% and a common signaling efficiency (i.e. number of slots carrying common signaling over total number of slots) up to 80.6% for the most stringent common signaling periodicity of 20 ms considered by 3GPP.