Prepare all ingredients: cube the white American cheese and cream cheese, shred the Monterey Jack, dice the jalapeño, drain the tomatoes, and mince the garlic.
Place the evaporated milk and cream cheese in a medium saucepan over medium-low heat. Whisk until the cream cheese is fully melted and the mixture is smooth.
Gradually add the white American cheese a handful at a time, stirring constantly. Once it begins to melt, add the Monterey Jack cheese the same way. Keep the heat low and stir in a figure-eight motion until everything is silky.
Stir in the minced garlic, diced jalapeño, drained tomatoes, cumin, chili powder, and salt. Continue cooking and stirring for 2–3 minutes until fully combined.
Check the consistency. If the queso is too thick, add a splash of milk. If too thin, simmer gently for another minute while stirring.
Transfer to a serving bowl, garnish with green onions and cilantro, and serve immediately with tortilla chips.