In the bowl of a food processor, add the spinach, cilantro, onion, poblano pepper, jalapeƱo, garlic, and 1/4 cup of broth. Set it aside.
In a large pot, heat the oil over medium-high heat. Add the rice and cook, stirring, until it begins to brown, about two to three minutes. Add the green salsa and cook, stirring, until it becomes fragrant, about two to three minutes. Stir in the broth. Bring the mixture to a boil and reduce the heat to medium-low. Cover the pot and continue to cook until all of the broth has been absorbed, about 15 minutes. Stir in the beans and lime juice. Season with salt and pepper to taste.
Serve the rice immediately or store in the refrigerator for up to five days.