Heat 2 tablespoons extra-virgin olive oil in a skillet over medium heat then add chorizo.
While chorizo is rendering and browning, peel onion. Place meat in a mixing bowl. Grate a few tablespoons of onion directly over the meat. Quarter the remainder of the onion and thinly slice.
Add potatoes and onions to the chorizo. Season the hash browns with salt and pepper and fresh thyme. Once the potatoes are lightly browned, 7 to 8 minutes, flip them and press them down with a spatula to crisp them, continue to cook 7 to 8 minutes more.
To the sirloin, add parsley, smoked paprika, garlic, salt and pepper. Mix the burgers to combine and form 4 large patties. Create an indentation in each burger using the heal of your hand to counter the burger at the center that happens to burgers as they cook - your burgers will be nice and flat for topping if you use this trick!
Heat the remaining extra-virgin olive oil, 2 turns of the pan, in a large skillet over medium-high heat. Add the burgers to the skillet and cook 3 to 4 minutes on each side for medium rare burgers and up to 6 to 7 minutes on each side for well done. Melt manchego cheese, 2 thin slices on each burger, the last 2 minutes they are in the pan. Tent the skillet with loose foil to trap enough heat to melt the cheese.
Place pequillo peppers in food processor and add hot sauce, salt and pepper. Process the peppers into a smooth paste.
To assemble, place burgers on bun bottoms and top with sliced red onion, cucumber and tomato. Slather the bun tops with pepper paste and set into place. Serve crispy hash browns with chorizo along side.