Mexican-seasoned ground pork burgers. Adapted from Charcuterie: The Craft of Salting, Smoking, and Curing. Don't let the long list deter you. Chill time required. As for the cooking method, only 1 pan is needed.
To prepare the chorizo patties: Mix all the ingredients together until evenly combined. Cover with plastic wrap and refrigerate for at least 1 hour. Note: Can make this the day before.
To prepare the garlic shrimp: After peeling, deveining and rinsing the shrimp, dry them really well on a clean towel or paper toweling. Mix evenly with the remaining shrimp ingredients. Cover with plastic wrap and refrigerate for 30 min to 1 hour.
To prepare the paprika mayo: Mix all the ingredients together until even. Set aside.
To make the burger: Divide the chorizo-mixture into 4 equal portions, then shape into patties slightly larger than the buns.
Heat up 1 tablespoon olive oil in a large skillet over medium-high heat until sizzling hot, then add the butter until melted. To the pan add the chorizo patties (maximum 2 patties at a time). Leave the patties to pan-fry without moving, until a nicely browned crust has formed on the bottom. Turn the patties over, then add the shredded manchego cheese on top (2-3 tablespoons on each).
Cover the skillet completely with a lid and keep cooking on medium-high heat for another 1-2 min (the steam will melt the cheese as well as cook the patties), just until the center of the patties is cooked through. Transfer the patties onto a plate and let rest.
Keep the chorizo drippings in the skillet and cook the shrimp on high-heat, about 1 min on each side until just cooked through. Set aside.
If you want to toast the buns, remove any food-solids inside the skillet with a bit of oil left, then toast the cut-sides of the buns until golden browned in the same skillet.
Apply a generous layer of paprika mayonnaise on both sides of the buns, then put 2 thinly sliced tomatoes and a chorizo patty on top. Slice the shrimp lengthwise and place over the patty. Top with upper bun.