Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Line a baking sheet with aluminum foil. Place poblano peppers cut-side down on the prepared baking sheet.
Cook under the preheated broiler until the skin of the peppers has blackened and blistered, 5 to 8 minutes. Place blackened peppers into a bowl and tightly seal with plastic wrap. Allow peppers to steam as they cool, about 20 minutes. Remove and discard skins.
Heat 1 tablespoon oil in a medium saucepan over medium heat; cook onion and garlic until soft and translucent, about 5 minutes.
Combine poblano peppers, onion, garlic, water, cilantro, and lime juice in a blender; blend until smooth.
Heat remaining 1 tablespoon oil in a medium saucepan. Cook and stir rice, stirring frequently, until transparent, 2 to 3 minutes. Add poblano mixture and bring to a boil. Stir in chicken bouillon. Reduce heat to low, cover, and cook until rice has absorbed all liquid and is soft, about 20 minutes.
Remove rice from heat and fluff with a fork. Cover and let stand for 5 minutes before serving.