Preheat oven to 415°F (212°C)
On parchment paper roll out the dough into a large rectangle 13 x 11 inches (about 1/4 thick). Trim the edges to form a straight line and keep the trimmings.
Brush the olive oil on top of the dough, then evenly layer the pesto, feta and tomato leaving a small border around the edges, roughly 1/2 an inch wide.
Gently roll the dough into a log, then form it into a ring. Pinch the edges to seal. If the dough does tear, just patch it with any dough from trimming the edges.
Using a sharp knife cut slits along the outer edge of the ring (without cutting all the way through). Open the slits a little to expose the filling.