Combine the tomatillos, onion chunks, one-quarter of the bell pepper, the cilantro stems, jalapeño, garlic and 1 tablespoon olive oil in a blender. Puree until very smooth.
Heat a Dutch oven over medium-high heat. Add the remaining 2 tablespoons olive oil, then add the sliced onion and remaining bell pepper. Cook until slightly softened, about 3 minutes. Add the tomatillo puree and cook until thickened, 3 to 5 minutes. Add the chicken broth and 2 cups water. Bring to a simmer and season with 1/2 teaspoon salt. Add the rice, cover and simmer until al dente, about 13 minutes.
Add the shrimp to the pot and return to a simmer, then cover and turn off the heat, making sure the shrimp are completely submerged. Let stand until the rice and shrimp are cooked through, about 5 minutes; season with salt. Divide among bowls and top with cilantro leaves.