In a small bowl, whisk together 1/4 cup of the milk with 3 tbsp of cornstarch to create a slurry; set aside.

Heat a large saucepan on medium heat; when hot add oil. Add the onions, garlic, poblano, and jalapeño and cook until soft, about 5-7 minutes. Season with salt, to taste.

Add the chicken broth and the rest of the milk. Bring to a boil and cook for about 3 minutes to reduce slightly.

Add the slurry (cornstarch mixture) to the pan and stir; simmer a minute until it bubbles and thickens, then reduce heat to low.

Add the drained tomatoes, cilantro, lime juice, chili powder, cumin, salt, and pepper. Remove from heat and add the cheese; stir until it melts completely. Serve immediately.