Manchego-Stuffed Pork Burgers

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2 tablespoons vegetable oil, plus more for brushing

1/4 cup pimento-stuffed Spanish olives

4 cloves garlic

1 tablespoon dried oregano

1 tablespoon chili powder

2 teaspoons smoked paprika

1 teaspoon ground coriander

1 teaspoon ground cumin

1/2 teaspoon ground allspice

3 tablespoons mayonnaise

1 1/4 pounds coarsely ground pork

Kosher salt and freshly ground pepper

1/4 pound manchego cheese, broken into bite-size pieces

4 Portuguese rolls, split

Pimentos, tomato, red onion and/or lettuce, for topping