\underline{S}imultaneous \underline{t}ransmitting \underline{a}nd \underline{r}eflecting \underline{s}urface (STARS)-assisted systems have emerged to fill this gap by providing $ 360^{\circ}$ wireless coverage. In parallel, full-duplex (FD) communication offers a higher achievable rate through efficient spectrum utilization compared to the half-duplex (HD) counterpart. Moreover, two-way/bi-directional communications in an FD system can further enhance the system's spectral efficiency. Hence, in this paper, we propose a STARS-enabled massive MIMO deployment in an FD two-way communication network for highly efficient spectrum utilization, while covering the dead zones around the STARS. This model enables simultaneous information exchange between multiple nodes, while \emph{potentially} doubling the spectral efficiency (SE). By invoking the use-and-then-forget (UaTF) combining scheme, we derive a closed-form expression for an achievable SE at each user of the system considering both uplink and downlink communications based on statistical channel state information (CSI), while also accounting for imperfect CSI and correlated fading conditions. Moreover, we formulate an optimization problem to obtain an optimal passive beamforming matrix design at the STARS that maximizes the sum achievable SE. The considered problem is non-convex and we propose a provably-convergent low-complexity algorithm, termed as \underline{pro}jected \underline{gr}adient \underline{a}scent \underline{m}ethod (ProGrAM), to obtain a stationary solution. Extensive numerical results are provided to establish the performance superiority of the FD STARS-enabled system over the HD STARS-enabled and FD conventional RIS (cRIS)-enabled counterparts, and also to show the effect of different parameters of interest on the system performance.