8 ounces Spanish chorizo, finely diced
2 tablespoons extra virgin olive oil
2 tablespoons roughly chopped fresh oregano leaves
7 1/2 ounces (about 1 1/2 cups) all-purpose flour
3/4 teaspoon baking powder
1/4 teaspoon baking soda
1 teaspoon kosher salt
2 teaspoons sugar
5 large eggs, divided
2 tablespoons vegetable or canola oil (plus more for cooking)
12 ounces (about 1 1/2 cups) buttermilk
4 (1- to 2-ounce each) slices halloumi cheese
Combine chorizo and olive oil in a large non-stick or cast iron skillet over medium heat and cook, stirring constantly, until chorizo is crisp. Transfer to a bowl, making sure to get all of the excess oil.
Add oregano to chorizo and toss to combine. Wipe out skillet and set aside.
Combine flour, baking powder, baking soda, salt, sugar, 1 egg, vegetable oil, buttermilk, and half of chorizo mixture in a large bowl and whisk together until it forms a batter. There should be no streaks of dry flour, but plenty of lumps are okay.
Return skillet to medium-low heat, add 1 tablespoon vegetable oil, and heat until shimmering, about 1 minute. Add 2 halloumi slices (these will become the center of two pancakes). Cook until lightly browned on first side, about 1 minute. Flip halloumi and scatter a teaspoon of crisp chorizo on either side of each piece of halloumi.
Ladle a few ounces of batter on top of halloumi and chorizo, completely covering it. Cook pancake without moving until well-browned and crisp on first side, 2 to 3 minutes.
Carefully flip and cook until browned on second side, about 2 minutes longer. Transfer to a rack and set in a warm oven while you cook the remaining pancakes.
Repeat Steps 3 and 4 to cook remaining pancakes.
Heat another tablespoon of oil in the skillet and place over medium-high heat.
Break remaining 4 eggs into the skillet and cook until crisp on the bottom but yolks are still runny, about 1 1/2 minutes.
Serve pancakes immediately, topped with a fried egg and drizzled with remaining chorizo and chorizo oil.