In a large bowl whisk together the peanut butter, coconut milk, water, lime juice, 2 cloves of crushed garlic, ginger, soy sauce, fish sauce, red pepper flakes, jalapeños, and the cilantro until a smooth consistency. Set aside.
In a small pan with some olive oil quickly sauté the shrimp on both sides with remaining 2 cloves of crushed garlic and the red chili paste for several minutes. Remove from heat and set aside.
Brush the bottom of the crust with a light layer of olive oil or cooking spray. Divide and spread the peanut sauce on top of the pizza dough(s) or crust(s) evenly and to the edges.
Top with the cooked shrimp, cheeses, carrots, and green onions.
Place the pizzas one at a time on a stone or baking sheet if going in the oven OR right on the grill with grill grates and bake/grill for 8 minutes. If you don't have either you can place a sheet pan that with fit inside the BBQ grill.
Top with fresh chopped cilantro, peanuts and cut into slices.
Video
Notes
Feel free to use fresh jalapeños with seeds removed and diced small. I like the brine flavor sometimes using the pickled, but often just use fresh too.