I'd probably cut "shiplap" rabbets on the edges of each board, and attach them with one nail/screw in the center of each - preferably screwed from below so they don't show. That'd allow for cross-grain expansion/contraction.
Otherwise, you could glue up the oak panel, and glue and screw (from below) the front of it, and use slotted screw holes at the middle and back. That way, the front would stay flush, and the movement would all be towards the back.