Start by tossing your diced tomatoes in a small bowl with about a tablespoon of the minced shallot and half of your chopped cilantro. Give it a light stir and set it aside while you build the queso base. This little topping adds a cool, juicy contrast once it's spooned over the warm, melty dip. I like to let it sit for a few minutes so the flavors have time to mingle.
In a medium saucepan over medium heat, melt the butter until it's just bubbling. Add the remaining shallot, the chopped hatch chiles, the jalapeño, and the salt. Cook everything for three to four minutes, stirring occasionally, until the shallot turns soft and translucent. Your kitchen should start smelling incredible right about now, that smoky-sweet chile aroma is a good sign you're on track.
Sprinkle the flour over the chile mixture and stir it in, letting it cook for about a minute so it loses that raw flour taste. Slowly pour in the milk while stirring constantly to avoid lumps. Let the mixture simmer for around five minutes, stirring every so often, until it starts to visibly thicken up and coat the back of your spoon.
Remove the pan from the heat and stir in your shredded cheddar and pepper jack a handful at a time. Keep stirring until the cheese is fully melted and the sauce turns smooth and glossy. Fold in the rest of your chopped cilantro at this point. Working off the heat here really helps keep the sauce silky instead of oily or stringy.
Pour the finished queso into your serving bowl and spoon that reserved tomato-shallot mixture right on top. Grab a big bowl of tortilla chips and serve immediately while everything is still warm and gooey. This dip is best enjoyed the moment it's ready, so have your chips standing by.