A new hybrid digital/analog scheme is proposed for lossy transmission of a Gaussian source over a two-receiver bandwidth-matched Gaussian broadcast channel with source side information available at each receiver. The proposed scheme makes use of a new level of freedom for point-to-point transmission and combines two previously known schemes that are optimal under two different conditions regarding channel and side information quality parameters. It is shown that for the entire intermediate region in the parameter space sandwiched between those two conditions, the proposed scheme can achieve the same distortion-power tradeoff as in point-to-point transmission simultaneously for both channels, and is therefore optimal.