In a large saucepan, heat the olive oil over medium-high heat.
Saute onions in oil for about 5 minutes until softened, stirring occasionally. Add in garlic and cumin and let toast for 1 minute.
Pour in chicken broth and season with salt. Add in diced poblanos. Heat to a simmer.
Pour in heavy cream. Use a stick blender to puree, or transfer to a blender to puree and return pureed soup to saucepan.
In a small bowl, toss shredded cheese with cornstarch. Over medium heat stir cheese into the pureed soup until melted. Heat until cheese is completely melted and soup thickens slightly.
