Preheat the oven to 450 degrees F. Line a baking sheet with parchment paper and lay the poblano peppers on top. Roast the peppers in the oven for 15-20 minutes, until the waxing skin bubbles up over the surface of the poblanos.
Meanwhile place a large saucepot over medium heat and add the butter, onions, garlic, cilantro, salt and cumin. Saute for 5-6 minutes. Then add the broth to the pot.
Once the poblano peppers are out of the oven, carefully peel off the waxy exterior. Remove the stems and seeds and place the flesh of the peppers in the pot. Bring the soup to boil. Then lower the heat and simmer for 20 minutes.
Shred or crumble the cheese and toss with the corn starch. Add it to the soup base and stir to melt the cheese. Then use an immersion blender to puree the soup until smooth and creamy. Salt and pepper to taste.
Serve the soup as-is with a slightly rustic texture, or use a food mill to strain the soup for a fine creamy texture. Serve warm.
NOTE: If you can't find a Mexican cheese that is good for melting, use monterey jack cheese. You can also pour the soup base into a standard blender if you don't have an immersion blender, but be very careful. Open the vent in the lid so the heat can escape, then cover the lid with a kitchen towel to protect yourself before pureeing. Exploding hot soup is not a good thing!