To prepare pizza dough, put flour, water, egg, salt, brown sugar and yeast in the pan of a bread machine. Choose the quick dough cycle or run the regular dough cycle for 10-15 minutes or until the ingredients have come together into a well kneaded ball of dough. Add more flour or water as necessary. Turn off the machine and allow the dough to rise in the pan, with the lid down, for 30 minutes or until doubled in size. The dough can also be made by hand or with a stand mixer and dough hook. Cover and let dough rise for 30 minutes.
While the dough is rising, peel the onions, halve and thinly slice. Heat olive oil in a large skillet over medium heat and cook onions, covered, stirring occasionally until caramelized and golden brown – about 15-20 minutes. Remove onions to a plate or small dish and set aside.
Once dough is ready, place it onto a lightly floured work surface and separate into two equal pieces. Roll one portion of dough into a 12-inch round shape and slide onto a flat baking sheet. Brush the top of the dough with olive oil. Repeat with the second piece of dough or freeze in a freezer bag for up to a month.
Using both hands, lift the dough off of the baking sheet and place, oiled side down, onto the grate of a moderately hot barbeque grill and grill until the underside is golden brown and has char marks, about 3-5 minutes. Brush the top of the dough with olive oil as it grills.
When grilled, carefully flip and slide the pizza dough, grilled side up, onto the baking sheet and top with caramelized onions, blue cheese, toasted walnuts and parsley. If making two pizzas, be sure to reserve half of the toppings for the second pizza.
Slide the pizza back onto the grill, topping side up, and grill, covered, until the underside is golden brown and the cheese is partially melted, about 3-5 minutes. Transfer the pizza to a cutting board or back onto the baking sheet and cut into pieces. Repeat steps for a second pizza if necessary. Serve immediately.
Makes 2 , 12-inch pizzas.
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