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.
Combine 4 poblano peppers, 1 cup chicken broth, onion, and garlic in a blender; blend until smooth.
Heat oil in a saucepan over medium heat and fry the rice, stirring continuously, until evenly browned, 3 to 5 minutes. Add poblano chile mixture and remaining 2 1/2 cups chicken broth, epazote, and salt. Bring to a boil, cover, reduce heat to low, and cook until rice is soft and all the liquid has been absorbed, 20 to 25 minutes.
Slice remaining poblano chile and serve as a garnish with the rice.