Preheat the grill to medium high.
Lightly dust a work surface with flour and roll out the dough into two 14-inch circles. Set aside the dough on a large tray with parchment paper in between.
Remove the rind from the tallegio. Arrange the olive oil, tomato sauce, prosciutto, taleggio, olives and pesto in bowls with spoons as needed on a tray so that you can work quickly when topping the pizzas. You will cut off small pieces of the cheese and add to the pizza while cooking so a small knife, such as a butter knife, will work well here.
When ready to cook, brush one side of the rounds of dough with olive oil and drape, oiled side down, onto the grill. Within a minute, the dough will pufff slightly. Depending on the temperature of your grill, marks will begin to appear. Lift the dough with tongs to check. Once marks appear, rotate the dough 45-degrees and cook one to two minutes longer until a cross-hatch pattern appears. Brush the top of the dough with olive oil and flip to the other side. Working quickly, top your pizza with the tomato sauce, slices of prosciutto, olives, and cheese. Once the cheese begins to melt, after about 2 minutes, add the pesto. Remove the pizza from the grill with a pizza paddle and set aside. Repeat with the remaining dough and ingredients. Serve hot.