Preheat your oven to 400 F.
Pull any tough or damaged outer leaves off the Brussels sprouts, then thinly slice them across to the stem. Discard stems. Set aside.
Heat a large skillet over medium-high heat and add the olive oil. Add the chorizo and cook, breaking up and crumbling it, until cooked through and no traces of pink remain. Remove with a slotted spoon, leaving a good tablespoon or two of rendered fat in the pan. Drain on a paper towel lined plate or bowl. Return the skillet to medium-high heat and add a drizzle of oil if your chorizo didn’t render much fat. Add the Brussels sprouts, season to taste with salt and pepper and cook until softened and they start getting some nice char on them. Add the shallots and garlic and cook about 2 more minutes, until cooked. Add the vinegar and stir to combine, cooking about 1 more minute.
Line a baking sheet with tortilla chips, in a slightly overlapping single layer. Evenly spread out half the cheese on the chips, then top with the Brussels sprouts. Top the Brussels sprouts with the chorizo, then the rest of the cheese. Place in the oven for 5 to 10 minutes, until the cheese is melted and bubbling and starting to brown on the edges.