Saute vegetables. Heat 2 tablespoons of the olive oil in a large frying pan over medium-high heat. Add poblanos, onions, kale, and garlic and season with salt. Cook, stirring occasionally, until vegetables are tender and just beginning to brown, about 5 minutes. Let cool slightly.

Blend. Transfer sauteed vegetables to a blender. Wipe out the frying pan with a paper towel and return to the stove. Add the cilantro, broth, and measured teaspoon of salt to the blender and blend until smooth.

Toast rice. In the same frying pan, heat the remaining 2 tablespoons of oil over medium heat. Add rice and toast, stirring frequently, in the oil until the grains go from translucent to opaque, about 4 minutes.

Simmer. Add the pepper puree, stir to combine and bring to a boil. Reduce heat to low, cover tightly, and cook until the rice is tender, about 30 minutes.

Serve. Squeeze the lime over the rice and fluff with a fork to mix the lime juice and the green puree that has floated to the top back into the rice. Serve warm.