Heat the oil in a saucepan over medium heat. Add the onion and peppers and cook, stirring, until softened, about 5 minutes. Add the canned tomatoes and green chiles and bring to a simmer. Reduce the heat and stir in the processed cheese until smooth. Remove the pan from the heat and stir in the Cheddar, mozzarella, fontina and Parmesan until melted. If it is too thick, add room temperature milk to thin it out; if milk is needed, add it slowly, stirring in between additions to make sure you achieve the desired consistency.
Stir in the oregano, most of the jalapeno (saving a pinch or two for garnish), 3/4 cup of the pepperoni and half of the tomatoes.
Transfer the queso to a serving dish. Garnish with the remaining pepperoni, jalapenos, and tomatoes, as well as the basil leaves. Serve with pizza-flavored chips.