Char or roast the poblanos. Char the poblanos over a gas stove burner until blackened all over. Alternately, place the poblanos on a greased baking sheet under the broiler for 10 minutes, until blackened. Transfer the charred poblanos to a heat safe bowl covered with plastic wrap or to a ziplock bag. Once cool, peel as much of the skin off the peppers as you can and remove the stems.
Make the green broth. In the bowl of a food processor or blender carafe, combine the poblanos, serrano, onion, garlic, cilantro, parsley, 1 tablespoon of olive oil, and 3/4 cup of the water. Blend until very smooth, then set aside.
Rinse the rice. Place the rice in a fine mesh strainer and rinse really well with cold water until the water runs clean. Let the rice drain for 10-15 minutes.
Toast the rice. Heat the rest of the olive oil in a 4 qt dutch oven over medium heat. Once the oil is hot, add the rice and toss it well to coat it in the oil. Let the rice cook, stirring occasionally, for 6-8 minutes or until some of the grains are starting to turn golden brown.
Simmer. Pour in the green broth and the rest of the water and stir well. Season the rice with salt and pepper. Bring the rice to a simmer, cover the pot, lower the heat to low, and cook for 18 minutes. Remove the pot from the heat and let it rest for 10 minutes without removing the lid.
Finish the rice. Use a fork to fluff the rice and fluff in the peas. Cover for another 5 minutes and let the residual heat warm the peas. Finish the rice with the lime juice and season to taste with salt and pepper.