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 the 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 1 teaspoon of 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. 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. Spread a few tablespoons of the Cilantro Pesto over each pizza, top with a few slices of buffalo mozzarella, and then top with 4 shrimp and cilantro leaves. Place the pizza on the grill until the cheese melts. Serve hot.
Combine all ingredients in a food processor and process until smooth. Season with salt and pepper, to taste.
Brush each shrimp with oil and season with salt and pepper. Grill for 1 to 2 minutes per side or until just cooked through (shrimp will be opaque and turn pink).