Preheat oven to broil with rack about 10 inches from heat source. Melt butter in a large broiler-safe skillet over medium-high. Add poblano, and cook, stirring often, until tender, about 3 minutes.
Add flour, and cook, stirring constantly, until bubbly, about 1 minute. Whisk in milk; cook, whisking often, until mixture thickens, about 5 minutes. Stir in salt and cumin. Add processed cheese and 1 ½ cups of the Cheddar, stirring until melted, 1 minute. Stir in chicken and cooked pasta; remove from heat.
Sprinkle with remaining ½ cup Cheddar. Broil in preheated oven until cheese is lightly browned, about 4 minutes. Garnish with cilantro.
