Make the pizza bases:
- Preheat barbecue (or oven) to 450F (230C).
Make the white sauce:
- Whisk the yeast in the warm water with the sugar. Let it sit in a warm place, until the yeast mixture begins to foam up.
- Sift the flours and salt into a large bowl.
- Make a well in the middle, and drizzle over the olive oil.
- Pour in the yeast mixture, a little at a time, mixing it in with the flour, until all the mixture is used up and you have a soft dough. If the dough is too dry, add more water, a tablespoon (15 mL) at a time, until you get a soft, but not sticky dough. Dust your workspace with a little flour, and turn the dough out on it.
- Knead well for about 7-10 minutes, until the dough is smooth. Shape the dough into a ball, and place it in a well oiled large bowl. Cover with a damp towel and proof it for about 1-2 hours, until the dough has risen and doubled in volume. Gently knock back the risen dough and turn it out on to a floured surface. Divide the dough into 4 pieces (or 2 pieces if making large pizzas).
- Using the palm of your hand (or a rolling pin) flatten the dough into thin bases.
Make the grilled rosemary rubbed turkey:
- To make the roux, heat the butter in a heavy based pan, until melted.
- Add the flour and garlic powder, and cook out the flour for about 2–3 minutes, until the raw taste disappears.
- Gently pour in the hot milk in a steady stream, whisking constantly to make a smooth sauce. Simmer the sauce for about 2–3 minutes, or until thick and creamy. Season to taste.
Assembling and grilling the pizza:
- Rub the turkey fillet with the chopped rosemary and salt and bring it up to room temperature.
- Brush with the unscented oil and place on the preheated barbecue. Grill the fillet for 8–10 minutes, then turn it.
- Brush with more oil, then continue grilling for another 10 minutes or so, until the turkey is cooked all the way through, and the juices run clear. The grilling time for the turkey will be based on how thick your fillet is.
- Rest the turkey fillet for about 5 minutes, then shred it.
- Place the pizza base on a well floured pizza peel. Gently flick it directly on to the preheated barbecue and grill for 1–2 minutes, until it starts to bubble up.
- Using the peel, take it off the barbecue and flip the base over on to a plate or chopping board. On the grilled side, spread some of the white sauce.
- Top with the shredded turkey, the sliced Shitake mushrooms and the picked rosemary leaves.
- Turn down the barbeque to 400F (230C).
- Slide the pizza back on to the barbecue grill, away from direct heat, and cover and grill for about 3–4 minutes, until the pizza is crisp on the bottom.
- Slide off the barbecue, and top with the shaved parmesan or pecorino cheese and drizzle with a little truffle oil to serve.
You can also use a preheated heavy duty pizza stone on the barbecue. If using a stone, top the pizza before sliding on to the stone and cook for about 7–8 minutes, or until the pizza is crisp on the bottom.