To make the pizza dough, in a small bowl, mix the lukewarm water, yeast, and sugar until well combined. Leave in a warm place for 5 minutes or until frothy. Stir in the olive oil.
In a large mixing bowl, whisk together the flours and salt.
Pour the yeast mixture over the dry ingredients and use your hands to bring the mixture together to form a dough.
In an electric mixture with the dough hook attachment, add the dough and mix for about five minutes on slow speed until everything is just incorporated.
Lightly grease the inside of a clean dry bowl with olive oil and place the dough inside.
Place a tea towel over the dough and leave in a warm place for 60 minutes until the dough double in size. This will give the gluten structure and strength and the dough will become elastic.
When ready to make the pizza, set up the grill by placing coals on one side and lighting them. Rake the coals to create a flat even bed to create an even steady heat zone. Let the temperature reach to 475-500 degrees F. Place the pizza stone on the grill and let it heat up.
While the grill is warming up, prepare the pizza. Dust a clean work surface lightly with semolina flour. Use your fist to knock the dough back with one good punch to let any air out.
Divide the dough in half. Roll out the dough to a 12x8 inch oval with ⅛ inch thick. Save the extra dough for another pizza.
Transfer the pizza base onto a piece of baking paper so transferring the assembled pizza to the heated stone will be easier.
Prick the pizza base all over with a fork.
Spread the pesto over the pizza base, leaving a ½ inch border. Sprinkle the mozzarella over the pesto.
Add the zucchini blossoms, pancetta, and cut burrata pieces. Sprinkle with sea salt and freshly ground pepper.
Transfer the pizza onto the heated pizza stone. Cook the pizza on the grill for 7-10 minutes or until golden and crisp.
Use a pizza paddle, carefully transfer the pizza to a serving plate. Drizzle with a few drops of truffle oil and garnish with chive blossoms. Serve immediately.