Char the poblano pepper over a gas burner on medium-high for 5 to 6 minutes, turning every 30 to 45 seconds, until blackened all over. Cover and steam for 10 minutes, then peel, seed, and finely dice.

Warm the 1/2 cup whole milk and 1/4 cup water in a medium saucepan over medium-low heat until small bubbles form at the edges, about 2 minutes. Add the 16 oz cubed white American cheese a handful at a time, stirring each addition until melted, about 6 to 8 minutes total.

Stir in the diced roasted poblano, 2 minced chipotle peppers, 1 tbsp adobo sauce, 1/2 tsp cumin, and 1/2 tsp salt. Cook over medium-low heat for 2 minutes, stirring until uniform. Taste and adjust salt.

Remove from heat and stir in 2 tbsp chopped cilantro and 1 tsp lime juice. Pour into a warm serving bowl, drizzle with extra adobo sauce, and scatter a pinch of fresh cilantro over the top.