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 oil in a small pot over medium heat. Add rice and cook until transparent, 2 to 3 minutes.
Combine poblano chiles, water, and salt in a blender; blend until smooth. Pour over rice and bring to a boil. Reduce heat, cover, and simmer until the liquid has almost been absorbed, 20 to 25 minutes. Add crema and Chihuahua cheese and cook for another 5 minutes. Remove from heat and let stand covered for 5 minutes.