Make the sauce by mixing orange juice, lime juice, cilantro, garlic, oregano, cumin, salt and pepper in a blender or food processor and mix well. Add 1 cup olive oil slowly, while it's running, to make a smooth emulsified sauce.
Pat the tenderloin dry and season with a little salt & pepper. Add to a large ziplock bag and pour in 3/4 cup of the sauce. Turn to coat pork on all sides and let marinate in the fridge overnight. Save remaining sauce for use later.
Preheat oven to 500F. Remove the pork from the marinade and pat dry (discard marinade). Heat a large oven-proof skillet over medium-high heat. Add 1 Tablespoon olive oil. When hot, sear the pork on all sides until browned. Transfer the pan to the oven and roast until the thickest part of the pork reaches 155F (about 20-30 minutes). Transfer to a plate and cover with foil and let rest for about 10 minutes). Cut into 8-12 slices
To assemble the sandwiches, spread 1 piece of bread with mustard. Top with pork, lightly brushed with some of the sauce. Top with ham, cheese and pickles. Spread prepared sauce on 2nd piece of bread and put on top, pressing slightly to adhere everything. Butter both outside sides of sandwiches. Heat a skillet or griddle over medium heat and add sandwiches. Press down with a spatula or heavy pan. Flip and repeat on other side until cheese starts to melt. Serve warm.
Nutrition Info Per Serving: Calories 957 Total Fat 62 g Cholesterol 184 mg Sodium 2382 mg Potassium 1080 mg Total Carbohydrate 42 g Dietary Fiber 4 g Sugars 5 g Protein 58 g