Preheat a grill to medium-high. Place the 2 tablespoons vegetable oil, the olives, garlic, oregano, chili powder, paprika, coriander, cumin and allspice in a food processor; pulse until smooth. Scrape the mixture into a large bowl and stir in 2 tablespoons mayonnaise.
Mix the pork into the olive mixture; season with salt and pepper. Shape into 4 patties, about 1/2 inch thick. Make a deep pocket in each; stuff with some manchego, then close the patty around the cheese.
Brush the burgers with oil; season with salt and pepper. Brush the grill with oil; grill the burgers until marked on the bottom, 5 minutes. Flip and continue grilling until just cooked through, 5 more minutes.
Brush the cut sides of the rolls with the remaining 1 tablespoon mayonnaise; grill until lightly toasted. Serve the burgers on the rolls with your choice of toppings.