Divide dough into 8 equal portions. On a lightly floured surface roll each portion to 1/4-in. (5-mm) thickness, 4 x 8-in. (10x20-cm) rectangles. Along the lengthwise halves of the rectangles -- leaving a 1/2-in.(1-cm) border at the edges -- sprinkle half the cheese and all the pepperoni slices. Lay a metal skewer (or 2 wooden skewers for sturdiness) onto the filling, extending along length of dough.
Working along the length, carefully fold dough over the filling, patting out air bubbles and tightly sealing edges. Place on parchment-lined baking sheet. Brush both sides of dough with oil.
Grill skewered dough on barbecue preheated to medium-high, 3 to 4 min. per side, turning, until dough is golden. Spoon tomato sauce onto top sides and sprinkle with remaining cheese. Continue grilling, covered, for 1 to 2 min. until cheese is melted and bubbly. Sprinkle with oregano.