Melt the butter in a heavy-bottomed Dutch oven over medium heat. Saute the onion and peppers until they are soft, roughly 5 minutes, stirring occasionally with a large wooden spoon.
Add the minced garlic and the tomatoes and cook until fragrant, roughly a minute, while constantly stirring.
Pour in the whole milk and heavy cream while whisking, then sprinkle in the chipotle pepper powder.
In a small bowl, make a cornstarch slurry by mixing equal parts water to cornstarch. Mix with a fork until smooth, then gradually add it to the hot milk mixture, whisking constantly. The cornstarch will make the sauce glossy.
Whisking constantly to prevent lumps or burnt spots, bring the sauce to a slight boil over medium heat, then reduce the heat and let it simmer until it starts to thicken. This will take roughly 12 to 15 minutes. (It will thicken more once the cheese is added and the sauce has cooled down a bit.)
Remove the Dutch oven from the heat and stir in the grated cheese in batches until it is melted.
Taste then add enough salt to your liking. Adjust other seasonings, if necessary.
Serve while warm. Keep the sauce warm by turning the stove to the lowest setting or transfer the copycat Chipotle queso blanco to a crock pot and keep on the warm setting.