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Combine the cilantro, olive oil, red wine vinegar, garlic, red pepper flakes, cumin, and salt in a food processor. Puree until a semi-chunky, pesto-like sauce forms. Scoop out into a small bowl and set off to the side.
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Preheat the grill to high heat/flame while you assemble the sandwiches.
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Slice each sandwich roll in half width-wise. Spread an equal bit of mustard on each bottom slice and an equal bit of chimichurri on the top slice.
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Cover the chimichurri with a slice of Swiss cheese and then cover the bottom mustard half with a few pickle slices. Layer two ham slices on top of the pickles and then about 1/2 cup of pulled pork over the cheese.
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Fold top half over the bottom half.
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Spray the grill with a little non-stick cooking spray. Place two sandwiches on the grill at a time, top side down. Cover with a cast iron skillet. Press down slightly.
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Cook for three-five minutes until charred and golden. Flip sandwich.
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Cover with cast iron. Cook for another 3-5 minutes. Remove from heat and do the same with two remaining sandwiches.
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Let panini's rest for 5 minutes before slicing or eating. Serve with more chimichurri on the side for dipping.