How to Make It
In a small bowl, whisk the water with the yeast and sugar. Let sit until foamy, about 10 minutes.
Using a stand mixer fitted with the dough hook, mix the flour with the salt and the yeast mixture at moderate speed until a smooth dough forms, about 10 minutes. Oil a large bowl and transfer your dough to the bowl. Lightly cover the dough with a sheet of plastic wrap and let sit at room temperature until doubled in size, about 30 minutes.
Meanwhile, in a small bowl, whisk the tomato sauce and paste with the dried oregano. Season with salt.
Light a grill and oil the grate. Invert a baking sheet and dust with semolina. Divide the dough in half. On a lightly floured work surface and using a lightly floured rolling pin, roll out each piece of dough to a 12-inch round.
Working with one round of dough at a time, transfer to the prepared baking sheet and then carefully slide the dough directly onto the grill. Grill the pizza until it is lightly charred on the bottom, about 2 minutes. Flip the pizza and then spread some of the sauce on the crust, leaving a 1-inch boarder. Be careful not to use too much sauce or your pizza will get soggy. Top with half of the blue cheese, cover the grill and cook until the bottom of the dough is lightly charred and the cheese is beginning to melt. Transfer the pizza to a work surface and top with half of the prosciutto, walnuts, arugula and torn basil. Repeat with the remaining dough round and toppings. Slice the pizza and serve.