Add 1 cup cilantro leaves, serrano pepper, garlic cloves and 1/4 cup of chicken broth to a blender. Blend until mixture is pureed. Set aside.
In a large pot, heat olive oil over medium-high heat. When hot, carefully add chicken thighs and drumsticks, skin-side down. Cook on first side for 4-5 minutes, and until skin is crisp and slightly browned. Flip and cook for an additional 5 minutes. Remove from pot and set aside.
If the chicken absorbed all of the oil, add a teaspoon of olive oil. If it released too much fat, pour it out, reserving about a teaspoon. Add yellow onion and cook until translucent, about 3 to 4 minutes. Next, add red bell pepper and ground cumin, allowing to cook for 1-2 more minutes.
Add the rice and cilantro liquid mixture to the pot and mix, being sure to completely coat the rice. Gently add the chicken back to the pot and cover with about 3 1/2 cups of chicken broth. The broth should almost cover the chicken. Bring the soup to a simmer and then immediately turn the heat down to medium low. Cover the pot and cook for 20-30 minutes, and until rice is fully cooked.
Add the remaining 1/2 cup cilantro leaves to the blender and 1/4 cup chicken broth. Just before serving, add the mixture to the soup. This will give it a bright green color.
When you’re ready to serve, add salt to taste. This will all depend on how salty your chicken broth was. I needed to add about 1 1/2 teaspoons of kosher salt. Mix in corn right before serving.
Add a few cilantro leaves to each bowl of soup, along with a few wedges of lime. It’s important.