Preheat a grill to medium and lightly oil the grates with the olive oil.
Dust a clean work surface with the flour, and roll the dough out into a 12-inch circle. Transfer the dough to a pizza peel or the back of a large baking sheet, and slide the dough onto the hot grill. Cook, without turning, until well marked and cooked on 1 side, about 3 minutes. Turn the dough over and quickly spread the pesto over the dough in a thin, even layer. Lay the prosciutto slices over the pesto, then sprinkle the cheese evenly over the prosciutto. Continue to cook, rotating the dough every 30 seconds or so, until the cheese is melted and the bottom of the crust is well-marked and cooked through, 3 to 4 minutes.
Remove from the grill, cut into 6 slices and serve immediately.
In a large bowl combine yeast with water and sugar and stir well to combine. Set aside until foamy, about 5 minutes. Add the salt, olive oil, and half of the flour and mix well to thoroughly combine. Add all remaining flour except 1/2 cup and mix well with your hands, working to incorporate the flour little by little. The dough should be slightly sticky to the touch. Transfer dough to a lightly floured work surface and knead dough for at least 5 and up to 7 minutes, adding enough additional flour, as necessary, to form a smooth and elastic dough that is not sticky. Transfer dough to a lightly oiled 2 or 3 quart bowl and turn to coat with oil. Cover with a damp towel and let rise in a warm place until doubled in size, usually at least 1 hour.
This is enough topping ingredients for 1 pizza, but the pizza dough makes enough for 2 pizzas...you could double the topping ingredients and change this to yield 2 pizzas if you like.