For the rub: Put the anchovies, oil, oregano, parsley, sage, thyme, lemon juice and some salt and pepper in a food processor, and buzz until combined into a puree.
For the pork: Preheat the oven to 275 degrees F.
Use your paring knife, and make cross-hatch slits straight down into the pork shoulder fat cap. Rub the anchovy herb rub over the pork shoulder getting it in each slit. Place the garlic cloves into the slits. Sprinkle with salt and pepper. Place in the oven until fully cooked and tender, 5 hours.
Remove from the oven and let it rest for 10 minutes, and then thinly slice. Save some pork fat from the rendering process to toast your bread.
For the aioli: Combine the mayonnaise, olives, parsley, capers, lemon zest, lemon juice and some salt and pepper in a bowl, and mix well.
For the sandwich build: On the toasted ciabatta, spread some aioli and place the thinly sliced pork shoulder on top. Garnish with pequillo peppers, then eat that bad boy like he's going out-a-style!