In a small bowl or mug, whisk together 1/4 c milk and cornstarch; set aside. Grease a large saucepan and heat over medium. Add the onion and poblano and sauté, stirring frequently, until the onion begins to become translucent, about 6-7 minutes.

Add the broth and remaining milk to the saucepan and simmer for about 5 minutes, stirring occasionally. Add the cornstarch mixture and reduce heat to low. Stir quickly until the mixture has thickened, about 1 minute.

Stir in shredded cheese and cook until melted, another 1-2 minutes. Add well-drained tomatoes, spices, cilantro and lime. Adjust seasoning to taste and serve immediately.