In a small saucepan, combine the vinegar, water, garlic, mustard seeds, sugar, and salt. Bring the mixture to a simmer over medium heat and stir until the sugar and salt dissolve.
Add the sliced red onions and jalapeño to the boiling pot of brine. Press them down, making sure the vegetables are completely submerged. Once the pot returns to a boil, cover it and turn off the heat, letting the pickles steam as they cool in the brine.
Preheat the oven to 375°F (190°C). Lightly oil a 12 x 7.5-inch (32 x 19 cm.) baking dish. Spread half of the Fritos into the vegan chili over the bottom of the prepared baking dish in an even layer. Spoon the chili over the chips.
In a medium mixing bowl, mix together the nacho cheese, corn kernels, hatch chiles, and shredded Mexican cheese.
Add the remaining Fritos and the vegan cheese corn topping to the casserole and scatter the diced tomatoes on top.
Bake for 25 to 30 minutes, until heated through and bubbling around the edges.
Let the casserole rest for 5 minutes before serving. Top with the pickled onions and jalapeños, vegan sour cream, avocado, cilantro, and lime wedges.