Melt butter in a saucepan over medium heat and add onion, green bell pepper, celery, jalapeno peppers, and green onions. Cook, stirring occasionally, until soft and slightly brown, about 5 minutes. Stir in flour until combined.
Reduce heat to low and add processed cheese food, pepper Jack cheese, milk, and heavy cream to the saucepan. Stir continuously until cheese is melted, about 10 minutes.