In a small bowl, whisk together the yeast and 1/4 cup of the warm water. Let sit for 5 minutes to proof. Place 1 3/4 cups of the flour in large bowl with the salt. Add the yeast mixture, the remaining water, and 2 teaspoons oil, and stir until combined. Transfer the dough to a floured surface and knead until smooth. Grease a large bowl with the remaining 1 teaspoon oil, add the dough and turn to coat. Cover and put in a warm place until doubled in volume, about 1 to 1 1/2 hours.
Preheat the grill to medium-high. Once the dough has risen, divide it in half, and set aside half for another use or for the Red Chile-White Anchovy Caesar Salad Pizza. Then divide the half into 4 balls. Roll each ball into 8-inch circles. Brush each circle with oil and grill on both sides until golden brown. Add 1/2 cup grated cheese to each pizza and grill until the cheese is just melted. Remove from the grill and spread a few tablespoons of the cilantro pesto over each pizza. Top each pizza with 4 shrimp and sprinkle with cilantro leaves.
Put all ingredients in the work bowl of a food processor. Process until smooth. Season with salt and pepper to taste.;
Preheat the grill to high. In a large bowl, toss the shrimp with enough olive oil to coat, and season with salt and pepper. Grill for 1 to 2 minutes per side or until just cooked through. Remove from grill and keep warm until ready to use.