For flatbread: Mix dry ingredients (flour, sugar, yeast and salt) and wet ingredients (water and vegetable oil) separately. Make a well in dry ingredients and mix in wet ingredients with a fork until dough is dry enough to handle. Knead dough until smooth. Cover with plastic wrap and let proof for 1 hour. Weigh out to four (4-oz.) portions and roll each portion into a ball. Roll out each ball with a rolling pin to a 10-inch diameter and place on floured parchment paper until all dough is rolled out. Grill each side of the flatbread, being careful not to burn it. After grilling, stack on top of each other at room temperature until ready to assemble.
For vegetables: Toss mushrooms in a bowl with 3 tbsp. olive oil and kosher salt. Place on the grill on medium heat. Once mushrooms have achieved a smoky flavor, about 1 to 3 minutes on each side, remove from grill and use hands to break into smaller pieces. To roast bell peppers, put on the grill at the highest temperature and char all sides. Place in a large bowl and cover bowl in plastic wrap for about 20 minutes. This will release the skin from the flesh. Peel off skins and remove seeds. Julienne peppers and set aside.
For pesto: Remove basil from stems, chop garlic and toast pine nuts. Place basil and garlic in a blender. Begin blending while slowly adding 1 cup olive oil. Add pine nuts, season with salt and pepper and purée until smooth.
To serve: Preheat oven to 350 degrees. Lay flatbreads out on a work surface. Spread about 1/2 cup of pesto on each, leaving 1/8 inch of crust all the way around. Distribute grilled mushrooms and roasted peppers evenly among flatbreads. Then lay pancetta slices over the top of everything. Place flatbreads in oven directly on the rack for about 5 minutes or until dough is crisp. Remove from oven and cut each into 6 slices.
Makes four (10-inch) flatbreads, Serves 8 to 10