Whisk together the yeast and 1/4 cup of the water in a small bowl and let sit for 5 minutes to proof. Place 1 3/4 cups of the flour in a large bowl with 1 1/2 teaspoons salt. Add the yeast mixture, the remaining water and oil and stir until combined. Transfer the dough to a floured surface and knead until smooth. Grease a large bowl with the remaining oil, add the dough and turn to coat. Cover and place in a warm place until doubled in volume, about 1 to 1 1/2 hours.
Preheat the grill to high. Once the dough has risen, divide it in half, and then divide each half into 2 balls. Roll each ball into an 8-inch circle. Brush with oil and grill on both sides until golden brown. Remove from grill and slice each in half horizontally.
Spread bottom halves of pizza with 3 ounces of the robiolo cheese and 2 ounces of the mozzarella. Season with salt and pepper. Place the tops on and heat on the grill for 30 seconds. Remove from the grill and drizzle each pizza top with a few teaspoons of white truffle oil. Slice into wedges and serve immediately.