Preheat the oven to 425 degrees F and place a rack on the second-to-top position. Line a rimmed baking sheet with foil leaving a 2-inch overhang on each side. Set aside.
Heat the oil in a large straight-sided skilletover medium-high heat. Add the beef and chorizo and break up the meat using the back of a wooden spoon or spatula. Sprinkle liberally with salt and black pepper and cook until browned but not fully cooked through, 4 to 6 minutes. Transfer the meat to a plate using a slotted spoon.
Add chiles and onions to the skillet with the rendered fat and cook until lightly browned and softened, stirring occasionally, 6 to 8 minutes. Stir in the chili powder, cumin, garlic and 1/4 cup water and cook for 2 minutes, stirring constantly. Add the tomato puree, beef stock, Worcestershire sauce and reserved browned beef and chorizo. Stir to combine and bring to a boil, and then lower to a simmer and cook covered for 25 minutes. Stir in the jalapeno pickling liquid and beans and cook for another 15 minutes, uncovered, until the chili has reduced slightly and is nice and thick. Season with salt and black pepper. Turn off the heat and cover with a lid to keep warm while you prepare the cheesy tortilla chips.
Spread the tortilla chips onto the prepared baking sheet in a single layer, allowing some overlap. Scatter the Cheddar and manchego evenly on top and bake until the cheese is melted and the chips are warmed through, 2 to 3 minutes.
To assemble, spoon the warm chili evenly all over the chips, top with dollops of sour cream and garnish with pickled jalapenos and sliced scallions. The nachos can be served directly on the baking sheet or you can lift the foil onto a large platter.