In a medium saucepan, melt butter over medium heat. Stir in flour and cook for 1 minute, stirring constantly, until a smooth paste forms.
Gradually whisk in milk, stirring constantly to avoid lumps. Cook for 2-3 minutes until the mixture thickens slightly.
Reduce heat to low. Add shredded white American cheese and Monterey Jack, stirring gently until fully melted and smooth, about 3-4 minutes.
Stir in diced green chiles, cumin, and cayenne pepper (if using). Taste and add salt as needed.
Transfer to a serving bowl, garnish with cilantro if desired, and serve immediately with tortilla chips or veggies.
