Cut the kidneys in half lengthwise and cover in a bowl with the milk and Worcestershire sauce. Add the mustard powder and cayenne. Let rest in the refrigerator overnight.
Preheat the oven or a pizza oven to 425 degrees F.
Sprinkle the flour in a bowl with salt and pepper. Remove the kidneys from the milk and dredge in the seasoned flour.
Add the butter to a 12-inch cast-iron pan over medium-high heat and let melt. Add the kidneys and sear for 3 to 5 minutes. Flip the kidneys, then transfer the pan to the oven to roast for another 5 minutes. Remove to a plate and let cool.
In the same cast-iron pan, heat 2 tablespoons oil. Add the onion and transfer to the oven to soften and begin roasting, about 5 minutes. Remove from the oven and let cool. Reserve the cast-iron pan for cooking more later.
Add the sliced potatoes to a baking sheet, then drizzle with 1/2 cup olive oil and sprinkle heavily with salt and pepper. Toss to combine, then add another tablespoon or two of olive oil if needed to make sure each potato is coated. Put the baking sheet in the oven to begin softening and roasting the potatoes, about 5 minutes. Remove from the oven and let cool.
Add the eggs to a very large bowl and whisk until beaten and thoroughly combined. Add the cooled kidneys, onions and potatoes to the eggs and gently toss to combine. Add 1/2 cup olive oil to the cast-iron pan and carefully pour in the egg mixture, spreading it in the pan to create an even layer. Transfer the pan to the oven, then cover with a lid (or baking sheet if you don't have a lid) and let cook until set, 20 to 25 minutes.
Remove the pan to the stovetop. Invert a cool baking sheet on top of the pan and flip the pan over so that the tortilla transfers onto the baking sheet. Slide the tortilla back into the pan. Put back in the oven and continue to cook, uncovered, until the tortilla is light golden on the underside, tucking the edges under to give it a nice round shape, about 5 more minutes.
For the oregano aioli: Mix the mayonnaise, oregano, smoked paprika and sherry vinegar in a bowl and season with salt and pepper.
Slice the tortilla into wedges or squares and garnish with the aioli and fresh oregano.