On a lightly floured surface, roll the pizza dough into a large rectangle approximately 18 inches by 12 inches.
Spread the pizza sauce in a very thin layer all over the dough, leaving a 1/4-inch border of clean dough along the top and side edges.
Scatter the Parmesan evenly over the sauce. Layer the pepperoni slices evenly over the Parmesan. Scatter the grated mozzarella over the pepperoni.
Beginning at the bottom edge, roll the dough up like a jelly roll toward the top, taking care to roll as tightly as possible. When you reach the top clean edge of the dough, pinch together at the seam to seal closed. Transfer the dough to the refrigerator to firm, 15 to 20 minutes.
Oil a 9-by-5-inch loaf pan. Split the dough in half lengthwise, exposing the striped insides. Carefully lift up one half and lay it across the other half so the two pieces form an X. Working from the center out, twist each end until the two loose ends meet. Lift the twisted dough into the loaf pan, then cover with plastic wrap and let rise until nearly doubled in size, about 1 hour.
Position an oven rack in the center of the oven and preheat to 350 degrees F.
Brush the top of the babka with olive oil and sprinkle with Parmesan. Bake until golden brown, 40 to 50 minutes. Rest on a rack 15 minutes, then transfer the babka from the pan to the rack and let rest another 15 minutes before slicing.