In a medium saucepan, melt the butter over medium heat. Add onion and jalapeno until softened and the onion is translucent, about 4-5 minutes. Add garlic and stir for 30 seconds.
Slowly pour in half n' half and stir to combine. Allow to warm for 4-5 minutes over medium heat.
Gradually add in shredded American cheese and Monterey jack cheese. Continue to stir until all of the cheese has been added and melted, keeping the heat at medium.
Add the chopped Roma tomatoes and cilantro, stirring to combine.
The queso will be fairly runny at this point, but the longer is sits over medium to low heat the more it will thicken up.
At this point you can transfer to a bowl if it will be eaten right away, or you can transfer to a crockpot on low heat to serve over an extended period of time.
Serve warm with tortilla chips, veggies, or pour over burritos or enchiladas